IBPS SO Prelims 2025 Question Paper with Answers & Explanations

Explanation

The passage directly identifies the central irony in the third paragraph, noting that the game was marketed to promote entertainment and interpersonal bonding, but instead led to isolation, dependency, strained relationships, and addiction among its users.

Explanation

According to the passage, the widespread use of the online game led to severe behavioral and academic issues among young users. Children became addicted and struggled to manage their daily schedules, leading to declining grades, reduced participation, and a lack of discipline in school. At home, they exhibited increased irritability, behavioral problems, and spent significantly less time interacting with family members, resulting in strained domestic relationships.

Explanation

The survey conducted by the independent organisation revealed widespread adverse effects on users, highlighting extreme dependency, falling academic achievement, and strained family relationships. Based on these severe social and behavioral consequences, the organisation concluded that the harm outweighed the commercial profits and recommended a nationwide ban on the game.

Explanation

The passage notes that roommates found their relationships remained smooth only during active gaming sessions. Once the console was turned off, genuine conversations were reduced and interactions became minimal, highlighting how the game created superficial bonding during gameplay while fostering isolation and a lack of authentic interaction outside of it.

Explanation

According to the first paragraph of the passage, the market response to the game was immediate and overwhelming upon release. It rapidly accumulated users worldwide and generated 50 million dollars in revenue, leading to widespread industry recognition and establishing Company X as a dominant market player.

Explanation

The passage explicitly mentions that as children grew addicted to the game, their studies suffered significantly, and teachers observed falling grades, a decline in participation, and a visible drop in discipline in school.

Explanation

The original sentence reads: "What initially gave the company a toe hold in the international gaming market was now turning into a nationwide social concern." The blank is therefore filled by 'toe hold', option (c).

Explanation

In the passage, the phrase a major hit refers to the immense popularity, high profits, and widespread adoption achieved by the online game upon its release, making success the direct contextual synonym.

Explanation

In the passage, the verb raise is used in the sense of bringing up, elevating, or increasing the level of concern. The direct antonym of raise is lower, which means to decrease, reduce, or bring down in level, volume, or intensity.

Explanation

According to the final paragraph of the passage, the independent organisation conducted a large-scale investigation into the negative impacts of the game, including addiction, reduced academic performance, and strained family relationships. Based on these findings, the report concluded that the social costs outweighed the company's financial profits and explicitly recommended that the game be banned nationwide to protect the discipline, values, and future prospects of young users.

Explanation

(a) He insisted to go to the market even though he was not feeling well. Incorrect. Rule: after the verb 'insist', we use on + gerund (verb + ing). Correct form: He insisted on going to the market even though he was not feeling well. (b) She said she would rather stay home than going to the party. Incorrect. Rule: after 'would rather', we always use the base form of the verb, not the gerund. Correct form: She said she would rather stay home than go to the party. (c) The manager along with his team were present at the conference. Incorrect. Rule: when a singular subject is followed by phrases like 'along with', 'together with', or 'as well as', the verb agrees with the main subject, not the phrase. Correct form: The manager along with his team was present at the conference. (d) The players were congratulated for their outstanding performance. Correct. The passive voice structure (subject + was/were + past participle) is correctly used here. (e) All are incorrect — this does not hold, since option (d) is grammatically and contextually correct. Hence, the sentence in option (d) is the correct one.

Explanation

The sentence follows standard English grammar rules. It correctly employs the present perfect passive voice structure (has been + past participle verb), where the singular subject the meeting agrees with the singular auxiliary verb has been, followed by the past participle rescheduled and the adverbial phrase modifying the reason appropriately.

Explanation

In formal and academic English, data is treated as a plural count noun derived from the singular datum. Consequently, it correctly pairs with the plural verb show, ensuring proper subject-verb agreement.

Explanation

The verb aims agrees with the singular subject policy, and the prepositional phrase at improving correctly uses a gerund after the preposition at to indicate the purpose or objective.

Explanation

Verbs expressing demand, insistence, or recommendation take a that-clause in the subjunctive mood. In the mandative subjunctive structure (demand that + subject + base verb), the verb in the subordinate clause remains in its base or uninflected form, making "demanded that their wages be increased" grammatically correct.

Explanation

The verb congratulate takes the preposition on when referring to the event, occasion, or achievement being celebrated (congratulate someone on something). The sentence correctly follows standard prepositional usage and grammatical agreement throughout.

Explanation

In this context, the passage describes the country experiencing or confronting a sudden rise in disruptive security incidents. The past participle verb faced correctly collocates with a surge in threats to denote encountering a critical issue that requires immediate response and mitigation by authorities.

Explanation

In the context of security threats and hoax calls targeting transit systems, callers typically claim the physical existence or placement of hazardous materials on board. The term presence accurately describes the state of explosives being situated in a specific location, which directly triggers emergency inspection procedures by security authorities.

Explanation

In the given context, the passive construction indicates that authorities or ministers were provided with or collected the relevant details concerning the fake bomb threats. The past participle received correctly conveys that the necessary reports and information about these communications had reached the government officials for further assessment.

Explanation

In the context of dealing with hoax calls and false alarms, emergency checks and security deployments needlessly consume personnel and operational assets, meaning the act wastes security resources while diverting attention from actual threats.

Explanation

In the context of the sentence, law enforcement and investigative agencies conduct inquiries specifically to determine the origin or individuals behind criminal acts. The verb identify means to establish or ascertain the identity of someone or something, which fits grammatically after the infinitive marker to and contextually aligns with tracing the origins of the threats.

Explanation

In legal and formal contexts, laws, rules, and penalties are implemented and applied using the verb enforce. In the given sentence, stating that strict punishment will be enforced under existing laws accurately conveys that legal penalties will be rigorously executed against the perpetrators.

Explanation

The first statement describes an action taken over time (saving money), and the second statement represents the direct result or outcome of that action (buying a new laptop). The conjunction 'so' is used to connect a cause to its logical consequence.

Explanation

The first statement describes a diligent effort, while the second presents a contrasting, unexpected negative outcome. The conjunction "yet" functions adversatively to link two contrasting independent clauses, conveying the meaning of "nevertheless" or "even so" without altering the intended context.

Explanation

The second statement expresses a direct result or consequence of the condition stated in the first statement. The conjunctive adverb 'therefore' indicates cause and effect, logically linking the closure of the shop to the inability to purchase groceries.

Explanation

The paragraph follows a direct chronological progression tracing the history of computing. It begins with ancient foundations like the abacus and mechanical calculators, advances to the 19th-century Analytical Engine designed by Charles Babbage, moves into 20th-century electronic breakthroughs like the ENIAC, describes the subsequent miniaturization into personal computers, and concludes with 21st-century advancements such as smartphones and cloud computing. This establishes the logical sequence as B-D-A-C-E.

Explanation

Sentence A introduces the central subject, defining glucose and its role as the primary energy source. Sentence E follows directly by introducing how the body regulates these glucose levels using hormones like insulin. Sentence C uses the demonstrative phrase "Such regulation" to build on sentence E, explaining why maintaining stable levels is vital. Sentences B and D form a coherent pair detailing the consequences of imbalance, starting with the effects of low blood sugar in B, followed by the contrasting effects of high blood sugar in D introduced by the transition word "Conversely". This establishes AECBD as the logical order.

Explanation

Sentence B serves as the general introduction, establishing wheat as a widely cultivated staple food crop. Sentence A follows by describing its specific growth requirements, such as a cool growing season and a warm, dry period. Sentence E naturally follows A because the phrase these requirements directly refers to the climatic conditions mentioned in A. With sentence D fixed at the fourth position, sentence C logically concludes the paragraph by discussing the overall growth in wheat production achieved through modern agricultural techniques.

Explanation

Sentence A establishes the central theme by introducing technology as a defining force reshaping multiple domains. Sentence E naturally follows by characterizing this transformation as a rapid pace of change that brings both opportunities and challenges. Sentence B elaborates on these dual aspects by detailing convenience and efficiency alongside concerns regarding privacy and mental health. With sentence D fixed in the fourth position discussing the deep influence on human behavior, sentence C logically concludes the paragraph with a forward-looking statement on the necessity of balancing ongoing innovation with human values.

Explanation

In the question statement, "The teacher asked the students to show their homework notebooks," the word 'show' means to present, display, or exhibit. Checking the given sentences: (A) They went to see a show at the theatre — here 'show' means a performance or entertainment event, a different meaning. (B) His paintings are on show at the gallery — here 'on show' means on display/being exhibited, matching the sense of present/display. (C) The wound did not show any sign of infection — here 'show' means to exhibit or display signs, also matching the sense of present/indicate. So the word is used in the same sense as the question in both B and C, giving option (b) Both B and C.

Explanation

In the sentence, whole functions as an adjective meaning entire, complete, or all of something. Statement A uses whole to mean the entire matter or all aspects of the topic under discussion. Similarly, statement C uses whole to describe the entire class, signifying all of its members collectively. Both statements preserve the identical adjective sense of entirety seen in the original statement.

Explanation

In the sentence "She has a firm belief in honesty", the adjective "firm" denotes something strongly held, steadfast, and unwavering. In the sentence "The manager took a firm decision against corruption", "firm" is used in the identical sense of being resolute, decisive, and unyielding.

Explanation

In the context of the sentence, a report is typically missing, while a question asked about it is unexpected. Interchanging missing and unexpected restores grammatical accuracy and contextual coherence: The manager's unexpected question about the missing report seemed to abash him completely, leaving him speechless and visibly uncomfortable in front of colleagues. All other highlighted words are already correctly positioned.

Explanation

The main clause requires the past tense verb "began" followed by the base form verb "abate" after the particle "to" to form the full infinitive "to abate" (meaning to lessen in intensity or subside). Swapping the positions of C and D produces "the storm began to abate", which makes the sentence grammatically sound and contextually meaningful while preserving all other words in their correct places.

Explanation

The sentence requires the main verb decided after the subject the monarch, followed by the infinitive to abdicate. The phrase choosing a quieter life correctly pairs the indefinite article a with a consonant sound, contrasting with the monarch stepping down. The conjunction while appropriately introduces the simultaneous subordinate clause describing his successor preparing for immense responsibility. Interchanging A with D and C with F yields: The monarch decided to abdicate his throne, choosing a quieter life of service, while his successor prepared for immense responsibility.

Explanation

The sentence is grammatically and contextually correct in its original form. The noun collapse appropriately describes the failure of a financial institution, considered an aberration correctly conveys that the event was seen as an anomaly, and investor confidence along with stable market fit standard business and economic collocations seamlessly.

Explanation

In the context of the sentence, voters choose to abstain when they are unhappy with the choices, making citing dissatisfaction with both candidates the appropriate cause. Consequently, abstaining lowers the overall turnout and participation rates. Swapping positions C and F correctly establishes this cause-and-effect relationship.

Explanation

The original past continuous form 'was eating' does not fit the context, since the phrase 'Five years later' points to a future point in time rather than an already-completed past action. Present continuous tense is used to describe a fixed future plan or arrangement, which is the sense intended here, so 'am eating' is the correct replacement. 'Will have been eating' (future perfect continuous) would only be appropriate for an action continuing up to a specific future point, while 'has been eating' and 'had been eating' incorrectly suggest present-perfect or past-perfect continuity that does not match the intended future sense. Hence, the correct replacement is 'am eating'.

Explanation

The phrase have yet to + base verb is an idiomatic construction used to indicate that something expected or intended has not taken place up to the present moment. Therefore, replacing have been yet with have yet yields the grammatically sound sentence: I have yet to go to the flower exhibition at Delhi University.

Explanation

The correlative conjunction pair not only ... but also requires parallelism. In the given sentence, but also is followed by a prepositional phrase (with providing her links), so not only must also precede a prepositional phrase (by giving hints). Placing helped her before not only ensures that both elements being joined share the same grammatical form.

Explanation

Prepositions in English grammar are followed by pronouns in the objective case. In the compound object following the preposition between, the second pronoun must be in the objective form rather than the subjective form. While you functions as both a subject and an object pronoun, the first-person singular subjective pronoun I must be replaced with its objective counterpart me, making between you and me the grammatically correct construction.

Explanation

When expressing two sequential actions that occurred in the past, the action that took place first is expressed in the past perfect tense (had + past participle), while the subsequent action is expressed in the simple past tense. Since the train departed prior to the arrival at the station, "had left" correctly denotes the earlier past action alongside "reached" for the later action.

Explanation

Phosphorus binds to lake bottom sediments and remains sequestered there for extended periods. When environmental conditions shift, such as during seasonal stratification or bottom-water anoxia, this internally stored phosphorus is progressively re-released into the water column. This internal nutrient loading perpetuates eutrophication, algal blooms, and oxygen depletion over many years, sustaining the negative ecological impacts long after external inputs from runoff or wastewater have been curtailed.

Explanation

The passage explicitly states that the chloride plus water reaction introduces chloride through sources like road salts, mining, or industrial effluents, steadily increasing salinity. This rise in salinity alters lake water density and circulation patterns, which stresses organisms specifically adapted to freshwater environments and leads to declines in plant diversity and fish populations.

Explanation

Artificial aeration or using mechanical oxygenation devices to prevent fish suffocation is completely absent from the passage. While the text highlights that algal decomposition depletes dissolved oxygen and suffocates aquatic life, it restricts the discussed mitigation measures to watershed management, chemical monitoring, agricultural buffer zones, de-icing alternatives, and wastewater treatment rather than mechanical in-lake interventions.

Explanation

According to the passage, the chloride and water reaction steadily raises salinity, altering water density and stressing freshwater species. This results in declining plant diversity, shrinking fish populations, and water that acquires an unpleasant taste unsuitable for drinking or irrigation purposes. Conversely, elevated phosphorus levels trigger harmful algal blooms that block sunlight, deplete oxygen, and disrupt overall biodiversity rather than enhancing plant diversity.

Explanation

Phosphorus enters lake ecosystems through agricultural runoff containing fertilizers, as well as detergents and untreated sewage, making agriculture a direct contributor rather than an unrelated sector.

Explanation

According to the passage, unnatural increases in chemical elements like phosphorus and chloride severely alter the aquatic environment. Elevated phosphorus levels trigger algal blooms that deplete dissolved oxygen, leading to the suffocation of aquatic fauna. Simultaneously, rising chloride concentrations increase salinity and alter water circulation, which stresses freshwater species, causes plant diversity to decline, and shrinks fish populations while also rendering the water unfit for drinking and agricultural use. Consequently, chemical imbalances create chain reactions that undermine ecological health and degrade water resources essential for human utility.

Explanation

Implementing measures to protect lake chemistry is challenging because it requires high costs and disruptions to established practices. Farmers often resist reducing fertilizer application, and municipalities depend heavily on road salts for winter road safety, creating a persistent conflict between economic and practical necessities and ecological conservation.

Explanation

In the passage, "lower" is used as a verb signifying a decrease or reduction in oxygen levels. The direct opposite of decreasing or dropping a physical quantity or level is to raise or increase it.

Explanation

In Step VI of the arrangement, the word 'Incumbent' is third from the left end, so the correct answer is 'Third'.

Explanation

The arrangement follows two simultaneous rules at each step: Words are moved to the extreme left in ascending alphabetical order of their second letter: Relegating (e), Chronic (h), Dismantle (i), Incumbent (n), Doughty (o), Purview (u). Numbers are shifted to the extreme right alternating between the smallest and largest remaining numbers: 38 (smallest), 73 (largest), 43 (2nd smallest), 68 (2nd largest), 47 (3rd smallest), 56 (3rd largest).

Applying this to the given input: Input: 43 Purview 68 Chronic 73 Dismantle 47 Incumbent 38 Relegating 56 Doughty Step I: Relegating 43 Purview 68 Chronic 73 Dismantle 47 Incumbent 56 Doughty 38 Step II: Chronic Relegating 43 Purview 68 Dismantle 47 Incumbent 56 Doughty 38 73 Step III: Dismantle Chronic Relegating Purview 68 47 Incumbent 56 Doughty 38 73 43

In Step III, the numbers to the left of "Doughty" are 68, 47, and 56, giving a total of three numbers.

Explanation

The rearrangement follows a dual pattern at each step: Words are shifted to the extreme left in alternating order of length and alphabetical priority: longest word (Relegating, 10 letters), shortest word (Chronic, 7 letters), second longest (Dismantle, 9 letters), second shortest (Doughty, 7 letters), third longest (Incumbent, 9 letters), and third shortest (Purview, 7 letters).

Numbers are shifted to the extreme right in alternating numerical order: smallest (38), largest (73), second smallest (43), second largest (68), third smallest (47), and third largest (56).

Tracing the input step-by-step: Input: 43 Purview 68 Chronic 73 Dismantle 47 Incumbent 38 Relegating 56 Doughty Step I: Relegating 43 Purview 68 Chronic 73 Dismantle 47 Incumbent 56 Doughty 38 Step II: Chronic Relegating 43 Purview 68 Dismantle 47 Incumbent 56 Doughty 38 73 Step III: Dismantle Chronic Relegating Purview 68 47 Incumbent 56 Doughty 38 73 43 Step IV: Doughty Dismantle Chronic Relegating Purview 47 Incumbent 56 38 73 43 68 Step V: Incumbent Doughty Dismantle Chronic Relegating Purview 56 38 73 43 68 47

In Step V, looking at the numbers from the right end: 1st number from the right = 47 2nd number from the right = 68 3rd number from the right = 43

The number 2nd to the left of 43 is 38.

Explanation

The rearrangement machine operates on two alternating rules simultaneously: Words are moved to the extreme left in the order of longest word, shortest word, second longest, second shortest, and so on (with alphabetical order as the tie-breaker for words of equal length). Numbers are moved to the extreme right in the order of smallest number, largest number, second smallest, second largest, and so on.

For the given input: 43 Purview 68 Chronic 73 Dismantle 47 Incumbent 38 Relegating 56 Doughty

Word lengths: Relegating (10 letters), Dismantle (9 letters), Incumbent (9 letters), Chronic (7 letters), Doughty (7 letters), Purview (7 letters).

Order of word movements (to the left): Relegating (longest: 10) Chronic (shortest: 7, C < D < P) Dismantle (2nd longest: 9, D < I) Doughty (2nd shortest: 7, D < P) Incumbent (3rd longest: 9) Purview (3rd shortest: 7)

Order of number movements (to the right): 38 (smallest) 73 (largest) 43 (2nd smallest) 68 (2nd largest) 47 (3rd smallest) 56 (3rd largest)

Tracing the steps: Step I: Relegating 43 Purview 68 Chronic 73 Dismantle 47 Incumbent 56 Doughty 38 Step II: Chronic Relegating 43 Purview 68 Dismantle 47 Incumbent 56 Doughty 38 73 Step III: Dismantle Chronic Relegating Purview 68 47 Incumbent 56 Doughty 38 73 43

The sequence Purview 68 47 appears consecutively in Step III.

Explanation

Arrangement Logic: Words are moved to the left end in each step in ascending order of their second letter: Relegating (e), Chronic (h), Dismantle (i), Incumbent (n), Doughty (o), Purview (u). Numbers are moved to the right end in an alternating sequence of lowest, highest, second lowest, second highest, and so on: 38, 73, 43, 68, 47, 56.

Step-by-step arrangement from the given Input: Input: 43 Purview 68 Chronic 73 Dismantle 47 Incumbent 38 Relegating 56 Doughty Step I: Relegating 43 Purview 68 Chronic 73 Dismantle 47 Incumbent 56 Doughty 38 Step II: Chronic Relegating 43 Purview 68 Dismantle 47 Incumbent 56 Doughty 38 73 Step III: Dismantle Chronic Relegating Purview 68 47 Incumbent 56 Doughty 38 73 43 Step IV: Incumbent Dismantle Chronic Relegating Purview 47 56 Doughty 38 73 43 68

Counting positions from the right end in Step IV: 1st position: 68 (even number) 2nd position: 43 3rd position: 73 (odd number) 4th position: 38 5th position: Doughty (word) 6th position: 56 7th position: 47 (odd number) 8th position: Purview 9th position: Relegating 10th position: Chronic 11th position: Dismantle 12th position: Incumbent

The odd numbers located at the odd positions from the right end are 73 (3rd position) and 47 (7th position).

Sum = 73 + 47 = 120

Explanation

Position of the required element from the left end = 12 + 4 = 16th element.

Counting elements from the left in the given series: 1st to 5th: F, M, 9, 0, * 6th to 10th: Y, 7, U, F, G 11th to 15th: %, , 3, 2, 0 16th: 6

The 16th element from the left end is 6.

Explanation

The required pattern is Symbol followed by Consonant followed by Number.

Scanning the series for symbols and checking the subsequent elements: Y7: The symbol is followed by the consonant Y, which is followed by the number 7. #L1: The symbol # is followed by the consonant L, which is followed by the number 1.

No other combination in the given sequence satisfies this condition, giving a total of 2 such consonants.

Explanation

Scanning the series from the left end, the odd numbers encountered are 9 (first), 7 (second), and 3 (third). Thus, the third odd number from the left end is 3.

Scanning the series from the right end, the numbers encountered are 6 (first) and 1 (second). Thus, the second number from the right end is 1.

Sum = 3 + 1 = 4.

Explanation

From Statement I, A lives on an even floor and B lives on floor 4, so A is on floor 2 or 6. If A is on floor 6, E is on floor 7, and since the number of people above A equals the number below G, G is on floor 2. However, the occupants of floors 1, 3, and 5 remain undetermined among C, D, and F. Thus, Statement I alone is not sufficient.

From Statement II alone, the floor numbers for A and the others cannot be uniquely determined.

Combining both statements, since G is on floor 2 and D lives immediately above G, D must be on floor 3. Statement II also specifies C on floor 5 (below A = 6) and F on floor 1, eliminating any other configuration (if A were on floor 2, floor 5 could not be below A). Hence, A lives on floor 6 and D lives on floor 3, exactly three floors below A. Both statements together are necessary to answer the question.

Explanation

From Statement I, Jyoti is 3rd from the left end. Since Jyoti is 2nd to the left of Rajat, Rajat is 3 + 2 = 5th from the left end. Additionally, Rajat is immediately to the left of the person who is 10th from the right end, which places Rajat 11th from the right end (with total children = 5 + 11 - 1 = 15). Thus, Rajat's position is uniquely determined. Statement II does not specify which end Meena is counted from or whether Rajat is to her left or right, making it insufficient.

Explanation

From Statement I, Rohan's father is the brother of Meena's mother, establishing that Rohan's father and Meena's mother are siblings. Therefore, Rohan is Meena's cousin.

From Statement II, the father of Rohan's sister is Rohan's father. Since Meena's mother is the sister of Rohan's father, they are siblings, which also establishes that Rohan is Meena's cousin.

Since each statement independently determines the relationship, either statement alone is sufficient.

Explanation

The data even in both statements I and II together are not sufficient to answer the question.

Explanation

Arranging the boxes from top (7) to bottom (1) based on the given conditions gives: Position 7: Box A, Pink, Chocolate Position 6: Box B, Green, Berry Position 5: Box C, Red, Bottles Position 4: Box D, Brown, Pencil Position 3: Box E, Blue, Juice Position 2: Box F, Black, Toys Position 1: Box G, Yellow, Balls

The black box is at position 2 and the green box is at position 6. The number of boxes placed between them is 3 (boxes at positions 3, 4, and 5).

Box D is at position 4, so the number of boxes placed below box D is also 3 (boxes at positions 1, 2, and 3).

Explanation

Arranging the boxes from top (7) to bottom (1) based on the given clues: Position 7: Box A (Pink, Chocolate) Position 6: Box B (Green, Berry) Position 5: Box C (Red, Bottles) Position 4: Box D (Brown, Pencil) Position 3: Box E (Blue, Juice) Position 2: Box F (Black, Toys) Position 1: Box G (Yellow, Balls)

Box C is at position 5 and Box D is at position 4. Therefore, Box C is placed immediately above Box D, not below it.

Explanation

Arranging the seven boxes from position 7 (top) to position 1 (bottom) using the given clues:

Position 7: Box A (Pink, Chocolate) Position 6: Box B (Green, Berry) Position 5: Box C (Red, Bottles) Position 4: Box D (Brown, Pencil) Position 3: Box E (Blue, Juice) Position 2: Box F (Black, Toys) Position 1: Box G (Yellow, Balls)

When Box A and Box E are interchanged, Box A moves to position 3. The boxes located above position 3 are those at positions 4, 5, 6, and 7, giving a total of four boxes above Box A.

Explanation

Arranging the seven boxes from top (7) to bottom (1) based on the given conditions gives:

Position 7: Box A, Pink, Chocolate Position 6: Box B, Green, Berry Position 5: Box C, Red, Bottles Position 4: Box D, Brown, Pencil Position 3: Box E, Blue, Juice Position 2: Box F, Black, Toys Position 1: Box G, Yellow, Balls

The pattern relates each box to the item inside the box situated directly above it: Box D (position 4) is directly below Bottles (position 5). Box F (position 2) is directly below Juice (position 3). Following the same logic, Box B (position 6) is directly below Chocolate (position 7).

Explanation

Arranging the 7 boxes from top (7) to bottom (1) based on the given conditions: Position 7: Box A, Pink colour, contains Chocolate Position 6: Box B, Green colour, contains Berry Position 5: Box C, Red colour, contains Bottles Position 4: Box D, Brown colour, contains Pencil Position 3: Box E, Blue colour, contains Juice Position 2: Box F, Black colour, contains Toys Position 1: Box G, Yellow colour, contains Balls

Since the Pink colour box is at the topmost position (Position 7), zero boxes are placed above it.

Explanation

From the given information: N's spouse is U (female), who is the daughter of L and D, and the sister of G. G is married to P, and their children are A (male) and E (female). C (father) and R (mother) are the parents of N (male) and H (male). Since N is the son of R, any daughter of R is N's sister. N's spouse (U) is the wife of N, which makes her the sister-in-law (brother's wife) of R's daughter.

Explanation

From the given information: L (male) and D (female) are married. Their children are G (male) and U (female). G is married to P (female), and their children are E (female) and A (male). U is married to N (male), and their child is V (female). C (male) and R (female) are married, and their children are N (male) and H (male).

E's cousin is V (child of U and N). H is the brother of V's father, N. Therefore, H is the paternal uncle of E's cousin V.

Explanation

From the given relationships: L (father) and D (mother) have two children: a son G and a daughter U. U is married to N, which makes U the only paternal aunt of G's children. G is married to P, and their children are E and A (the only nephew of U). Therefore, P is the mother of A.

Explanation

From the given family relationships: U is the spouse of N and the only paternal aunt of E, while G is E and A's father (married to P). L and D are the parents of G and U, making L the paternal grandfather of A.

C and R are the parents of N and H. Since G is male, H is also male. The child of N and U is V, whose gender differs from G and H, making V female (N's daughter).

When V marries S, S becomes the husband of N's daughter, which makes S the son-in-law of N.

Explanation

Statement II is the course of action here, since it gives the corrective steps that should be taken, while statement I explains the causes behind the extinction and statement III discusses the aftermath of the problem. Since only II states a corrective action, only II is implicit.

Explanation

The study establishes that reversing the biological aging of major blood vessels provides significant rejuvenation benefits, demonstrating that the elasticity, health, and functioning of the vascular system are directly tied to the physiological aging process of an individual.

Explanation

Arranging the eight persons around the square table in clockwise order (positions 1 to 8): Position 1 (Corner, facing inside): H from Chennai Position 2 (Side, facing outside): B from Pune Position 3 (Corner, facing inside): C from Jaipur Position 4 (Side, facing outside): G from Mumbai Position 5 (Corner, facing inside): D from Hyderabad Position 6 (Side, facing outside): E from Bengaluru Position 7 (Corner, facing inside): F from Delhi Position 8 (Side, facing outside): A from Kolkata

From this arrangement: The person from Hyderabad is D (at position 5, facing inside). The person sitting immediately to the left of D is E (at position 6, facing outside). Since E faces outside, the direction to the left is counter-clockwise: the first person to the left of E is D (position 5), and the second person to the left of E is G (position 4).

Explanation

Arranging the eight persons around the square table based on the given conditions gives the following clockwise arrangement starting from a corner: Position 1 (Corner, facing in): H from Chennai Position 2 (Side, facing out): B from Pune Position 3 (Corner, facing in): C from Jaipur Position 4 (Side, facing out): G from Mumbai Position 5 (Corner, facing in): D from Hyderabad Position 6 (Side, facing out): E from Bengaluru Position 7 (Corner, facing in): F from Delhi Position 8 (Side, facing out): A from Kolkata

The relation follows the logic where each person is mapped to the city of the person sitting directly opposite: A at position 8 is opposite to G from Mumbai. E at position 6 is opposite to B from Pune. F at position 7 sits directly opposite to C, who is from Jaipur.

Explanation

From the given arrangement, persons at the middle of the sides face outside while persons at the corners face inside: Middle of sides (facing outside): G (Mumbai), E (Bengaluru), A (Kolkata), and B (Pune). Corners (facing inside): D (Hyderabad), F (Delhi), H (Chennai), and C (Jaipur).

The one from Delhi (F) sits at a corner facing inside towards the center. Moving clockwise from F corresponds to F's left: 1st to the left of F is A (Kolkata) 2nd to the left of F is H (Chennai)

Thus, H sits second to the left of the one who is from Delhi.

Explanation

From the given conditions, the arrangement of persons and cities around the square table is: Corner seats (facing inside): H from Chennai, C from Jaipur, D from Hyderabad, and F from Delhi. Middle seats (facing outside): B from Pune, G from Mumbai, E from Bengaluru, and A from Kolkata.

F, H, C, and the person from Hyderabad (D) all sit at the corners of the table and face inside towards the center. The person from Mumbai (G) sits at the middle of a side and faces outside, making it the odd one out.

Explanation

Evaluating the seating positions around the square table where corner positions face inside and middle-side positions face outside: Pune is at a middle position (facing outside) so that its immediate left is a corner. B sits at the middle from Pune, and C sits to B's immediate right at a corner from Jaipur. G sits at a middle position (two places away from Pune) and is from Mumbai. F sits at a corner (third to the right of G) and is from Delhi. H sits at a corner (one place away from Delhi) and is from Chennai. A sits at the middle (immediate right of H) and is from Kolkata (opposite Mumbai). D sits at a corner (third to the left of A) and is from Hyderabad. E sits at the middle adjacent to D.

Since B and D cannot be from Bengaluru, E is from Bengaluru.

Explanation

An implicit assumption is an unstated premise necessary for the statement to hold logical validity. When the government introduces a targeted relief package specifically directed toward farmers in response to widespread flooding, it presupposes that the farming community has endured substantial damage and represents one of the critically impacted segments requiring immediate state intervention.

Explanation

For a targeted policy intervention to reduce overall air pollution by regulating vehicles, there must be a direct causal assumption that vehicular emissions contribute substantially to the worsening air quality. Without this link, imposing stricter emission standards on vehicles would fail to impact pollution levels meaningfully.

Explanation

O is positioned 4th from the left end. Since V has one person between O and V, V is at position 2 or 6.

Let the total number of persons be N. The number of persons to the left of V equals the number of persons to the right of M. Since M is immediately left of H and H is third to the right of K, M is two places to the right of K and H is three places to the right of K. With at most 3 persons to the right of H, V must be at position 2, placing 1 person to the left of V and 1 person to the right of M, which makes H the last person at position N = pos(M) + 1.

The number of persons between G and B is 3, so the number of persons between G and O is 2 × 3 = 6. Since O is at position 4, G is at position 4 + 6 + 1 = 11.

Since G is an immediate neighbour of K and B is five places away from K with at most 3 persons between B and G, K is at position 12 and B is at position 7.

Consequently, M is at position 12 + 2 = 14, and H is at position 15. The number of persons sitting between M (position 14) and O (position 4) is 14 − 4 − 1 = 9.

Explanation

Position the individuals from left to right in a linear row facing north:

O sits fourth from the left end (position 4). Since one person sits between O and V, V can be at position 2 or position 6. If V is at position 6, there are 5 persons to the left of V, meaning 5 persons must sit to the right of M, which leaves 4 persons to the right of H, violating the condition that at most 3 persons sit to the right of H. Thus, V is fixed at position 2 (1 person to its left).

With 1 person to the left of V, exactly 1 person sits to the right of M. Since M sits immediately left of H, H is the last person in the row (position 15), M is at position 14, and the total length of the row is 15.

H sits third to the right of K, placing K at position 12. G is an immediate neighbour of K at position 11. B sits 5 places away from K to the left at position 7, leaving 3 persons between B and G, and 6 persons between G and O (satisfying 6 = 2 × 3).

Since M is at position 14, the person sitting seventh to the left of M is at position 14 - 7 = 7, which is B.

Explanation

Position O is 4th from the left end, so O = 4. Since B is 5 places away from K and G is an immediate neighbour of K with at most 3 persons between B and G, the number of persons between B and G must be 3. The number of persons between G and O is 2 × 3 = 6, which places G at position 11 (4 + 6 + 1 = 11). With G at 11 and 3 persons between G and B, B is at position 7, which gives K = 12. H sits third to the right of K, so H = 15, and M sits immediately left of H at position 14. One person sits between O and V, so V is at position 2. The number of persons to the left of V is 1, which equals the number of persons to the right of M. Thus, exactly 1 person sits to the right of M, making the total number of persons in the row 14 + 1 = 15.

Explanation

The word CONCEPTUAL has 10 letters: C, O, N, C, E, P, T, U, A, L.

Arranging these letters in alphabetical order gives A, C, C, E, L, N, O, P, T, U.

Placing them in alphabetical order starting from the right end gives: Original: C-O-N-C-E-P-T-U-A-L New order: U-T-P-O-N-L-E-C-C-A

Comparing each position from 1 to 10: Position 1: C and U Position 2: O and T Position 3: N and P Position 4: C and O Position 5: E and N Position 6: P and L Position 7: T and E Position 8: U and C Position 9: A and C Position 10: L and A

None of the letters remain in their original positions.

Explanation

The coding logic reverses the order of the letters in the input word and shifts their alphabetical positions forward by +2, +4, and +6:

Third letter + 2 gives the first coded letter: N (14) + 2 = 16 (P) Second letter + 4 gives the second coded letter: A (1) + 4 = 5 (E) First letter + 6 gives the third coded letter: H (8) + 6 = 14 (N)

Combining these positions yields the meaningful word PEN.

Explanation

From the given statement, evaluating the path between H and P: H > U ≥ E > N ≥ P Since the strictly greater sign (>) has the highest priority along the path, the resulting relation is H > P. Thus, conclusion I is definitely true.

Evaluating the path between P and S: P ≤ K ≤ R < S Since the strictly less sign (<) has the highest priority along the path, the resulting relation is P < S. Therefore, the relation P ≤ S does not follow.

Explanation

Combining the statements via the common element O: For Conclusion I, linking H > R with R > O and O = M gives the chain H > R > O = M, which establishes H > M. For Conclusion II, linking P ≥ M = O with O = T gives the chain P ≥ O = T, which establishes P ≥ T. Therefore, both conclusions are valid.

Explanation

To evaluate Conclusion I (Z ≥ J), combine the statements involving Z and J via common element T: Z ≥ T ≤ N = J. Since opposite inequality signs (≥ and ≤) appear between Z and J, no definite relationship can be established.

To evaluate Conclusion II (R < S), combine the path from S to R via T: S > W ≥ T ≤ N = J > R. Opposite inequality signs (> and ≤) meet at T, meaning no definite relationship exists between S and R.

Neither conclusion follows from the given statements.

Explanation

From the given statements, Y = A and I = B. Connecting A and B through common element V yields the path A ≥ R < V ≥ B. The presence of opposing inequality signs (< and ≥) means no definite relation can be established between A and B.

Substituting the equivalent variables into the conclusions gives A ≥ B for Conclusion I and A < B for Conclusion II. Together, these two conclusions exhaust all three possible relational states (greater than, equal to, or less than). Hence, they form a complementary pair where either conclusion I or II is true.

Explanation

Number 435673538: digits <6 (4,3,5,3,5,3) each -2 -> 2,1,3,1,3,1; digits >=6 (6,7,8) each -1 -> 5,6,7. New sequence by position: 2,1,3,5,6,1,3,1,7. Removing all digits that repeat (1 appears 3x, 3 appears 2x) leaves 2,5,6,7. Sum of odd digits (5+7=12) minus sum of even digits (2+6=8) = 4. Option (b).

Explanation

Arranging the eight persons from top to bottom (floors 8 to 1) according to the given clues yields: Floor 8: H (Philosophy) Floor 7: C (Hindi) Floor 6: B (Chemistry) Floor 5: A (Science) Floor 4: F (English) Floor 3: E (Biology) Floor 2: G (Physics) Floor 1: D (Mathematics)

A lives on floor 5, so the number of floors above A is 8 - 5 = 3. Let the required person live on floor k, so the number of floors below is k - 1. Given: 3 = (k - 1) + 1 => k = 3. The person living on floor 3 likes Biology.

Explanation

Placing G with Physics on floor 2 puts E on floor 3. With H on floor 8, the condition of three floors between H and English places English on floor 4. Consequently, Science is on floor 5 to balance the equal number of floors above English (4 floors) and below Science (4 floors).

Since more than two floors separate D from Science (floor 5), D must be on floor 1. Biology is two floors above D on floor 3 (E), placing Chemistry on floor 6 (two floors above Biology).

The consecutive group of C, Chemistry, and A places C on floor 7, Chemistry on floor 6 (B), and A on floor 5. Since F lives below A and three floors below Hindi (floor 7), F is on floor 4 and likes English.

Explanation

Arranging the persons and subjects on floors 1 to 8: Floor 8: H (Philosophy) Floor 7: C (Hindi) Floor 6: B (Chemistry) Floor 5: A (Science) Floor 4: F (English) Floor 3: E (Biology) Floor 2: G (Physics) Floor 1: D (Mathematics)

G lives on floor 2 and the one who likes Philosophy (H) lives on floor 8. The floor exactly midway between floor 2 and floor 8 is (2 + 8) / 2 = 5, where the person who likes Science lives.

Explanation

From the given conditions: G lives on floor 2 and likes Physics, with E immediately above on floor 3. H lives on floor 8, placing the one who likes English on floor 4 (three persons between H and English). With 4 persons above English, 4 persons must live below Science, placing Science on floor 5. The block of C, Chemistry, and A requires C on floor 7, Chemistry on floor 6, and A on floor 5 (so A likes Science). A lives above F, placing F on floor 4 (English), which is 3 floors below Hindi on floor 7 (C likes Hindi). Biology is 2 floors above Chemistry with two persons between them, placing Biology on floor 3 (E likes Biology), which means D lives on floor 1. Since D does not like Philosophy, H likes Philosophy, leaving D with Mathematics, and B on floor 6 with Chemistry.

The final floor arrangement from top to bottom (8 to 1) is: 8: H - Philosophy 7: C - Hindi 6: B - Chemistry 5: A - Science 4: F - English 3: E - Biology 2: G - Physics 1: D - Mathematics

Explanation

Working through the 8-floor puzzle clues gives the following arrangement: Floor 1 - D (Mathematics), Floor 2 - G (Physics), Floor 3 - E (Biology), Floor 4 - F (English), Floor 5 - A (Science), Floor 6 - B (Chemistry), Floor 7 - C (Hindi), Floor 8 - H (Philosophy). All the given constraints are satisfied by this arrangement. Statement I (E is above D's floor, i.e. 3 > 1) is true. Statement II (B likes Science) is false, since B actually likes Chemistry. Statement III (no one lives above H) is true, since H is on the topmost floor, 8. So only statement II is false, making the answer 'Only II'.

Explanation

The pattern relates the positional values of the first and last letters to the total length of the word: Code = (Positional value of first letter + Positional value of last letter) - Total number of letters

For PLAYER: P = 16, R = 18, Number of letters = 6 Code = (16 + 18) - 6 = 34 - 6 = 28

For NOISE: N = 14, E = 5, Number of letters = 5 Code = (14 + 5) - 5 = 19 - 5 = 14

Applying the pattern to HOCKEY: H = 8, Y = 25, Number of letters = 6 Code = (8 + 25) - 6 = 33 - 6 = 27

Explanation

Taking point M as the origin (0, 0), with the positive x-axis representing East and the positive y-axis representing North: Point Q is 6m east of M, so Q is at (6, 0). Point R is exactly between M and Q, which gives R at (3, 0). Point S is 6m south of R, so S is at (3, -6). Point T is 7m east of S, so T is at (3 + 7, -6) = (10, -6). Since T has a positive x-coordinate (East) and a negative y-coordinate (South) relative to M (0, 0), point T is in the south-east direction from point M.

Explanation

Set point M at origin (0, 0).

Point L is 15 m south of M, so L = (0, -15). Point Q is 6 m east of M, so Q = (6, 0). Point R is exactly between M and Q, so R = (3, 0). Point S is 6 m south of R, so S = (3, -6).

The shortest distance d between S(3, -6) and L(0, -15) is given by the distance formula: d = √((x₂ - x₁)² + (y₂ - y₁)²) d = √((3 - 0)² + (-6 - (-15))²) d = √(3² + 9²) = √(9 + 81) = √90 m

Explanation

Setting point M at origin (0, 0), the coordinates of all points are: M(0, 0) L(0, -15) N(-13, -15) O(-13, -6) Q(6, 0) R(3, 0) S(3, -6) T(10, -6) U(10, -17)

In each of the other pairs, the second point is located in the south-east direction with respect to the first point (positive change in x, negative change in y). For the pair formed by O(-13, -6) and T(10, -6), both share the exact same y-coordinate of -6, so point T lies directly due east of point O.

Explanation

Taking M = (0,0), L = (0,-15), N = (-13,-15), Q = (6,0), R = (3,0) (the midpoint of M and Q), and O = (-13,-6), the total distance from R to O is found by summing the given directional path: R to M (3 m) → M to L (15 m south) → L to N (13 m west) → N to O (9 m north), giving 3 + 15 + 13 + 9 = 40 m. Hence, the total distance from R to O is 40 m.

Explanation

B alone completes the whole work in 4x4=16 days. Efficiency is inversely proportional to time, so time ratio A:B = 2:1 and A alone takes 32 days. Total work = 32 units. 3x + 2x4 = 32 => 3x = 24 => x = 6.

Explanation

Watch: CP=750, profit 20% => SP=900, profit=Rs150. Bag: CP=840, loss 15% => SP=714, loss=Rs126. Net = 150-126 = Rs24 profit.

Explanation

Upstream speed is 15 km/hr, so the time taken to cover 105 km upstream is 105/15 = 7 hours. Since the ratio of upstream to downstream time is 7 : 6, the downstream time is 6 hours, which gives a downstream speed of 108/6 = 18 km/hr. The difference between the downstream and upstream speeds is 18 - 15 = 3 km/hr.

Explanation

Total time taken to meet from 10 AM to 3 PM = 5 hours. Relative speed of both cars = Total distance / Time = 660 / 5 = 132 km/hr. Let the speeds of car A and car B be S_A and S_B respectively. S_A + S_B = 132 km/hr S_A - S_B = 12 km/hr Adding the two equations: 2 × S_A = 144 S_A = 72 km/hr.

Explanation

Profit sharing ratio = (Capital × Time Period).

Ratio of profit of Abhi : Bhushan : Divya = (2000 × 12) : (3000 × 12) : (4000 × 4) = 24000 : 36000 : 16000 = 6 : 9 : 4

Given Divya's share = 4 units = Rs. 6000. 1 unit = 6000 / 4 = Rs. 1500.

Combined share of Abhi and Bhushan = 6 + 9 = 15 units. Total profit share of Abhi and Bhushan = 15 × 1500 = Rs. 22500.

Explanation

Side of the square = Perimeter / 4 = 96 / 4 = 24 cm Area of the square = 24² = 576 cm²

Using the area ratio of rectangle to square (7 : 6): Area of the rectangle = (7 / 6) × 576 = 672 cm²

Let the length and breadth of the rectangle be 21x and 8x respectively: Area = Length × Breadth 21x × 8x = 672 168x² = 672 x² = 4 x = 2

Dimensions of the rectangle: Length = 21 × 2 = 42 cm Breadth = 8 × 2 = 16 cm

Perimeter of the rectangle = 2 × (Length + Breadth) = 2 × (42 + 16) = 2 × 58 = 116 cm

Explanation

Initial quantity of mixture = 72 liters, with milk and water in the ratio 5 : 3. After removing 40 liters of mixture, remaining mixture = 72 − 40 = 32 liters. Quantity of milk in remaining mixture = (5 / 8) × 32 = 20 liters. Quantity of water in remaining mixture = (3 / 8) × 32 = 12 liters. When x liters of pure milk is added, the new quantity of milk is 20 + x, while water remains 12 liters. According to the condition, milk becomes 7 times the water: 20 + x = 7 × 12 20 + x = 84 x = 84 − 20 = 64 liters.

Explanation

Total orders delivered by Zomato across cities A, B, and C = 3 × 43 ⅓ = 130.

Let Swiggy orders in A = 5x and Zomato orders in B = 3x. Zomato orders in C = 20% of 5x = x. Swiggy orders in C = 3x + 20. Given that total orders by Zomato and Swiggy together in A is 150, Zomato orders in A = 150 - 5x.

Sum of Zomato orders: (150 - 5x) + 3x + x = 130 150 - x = 130 x = 20

Thus: Orders by Zomato in A = 150 - 5(20) = 50 Orders by Swiggy in C = 3(20) + 20 = 80

Required difference = 80 - 50 = 30

Explanation

The question directly states that the number of orders delivered by Zomato in C is 20% of the number of orders delivered by Swiggy in A.

Ratio of Zomato in C to Swiggy in A = 20% : 100% = 20 : 100 = 1 : 5

Explanation

Total orders delivered by Zomato in cities A, B, and C = 3 × (43 1/3) = 130.

Let Swiggy orders in A = 5k and Zomato orders in B = 3k. Zomato orders in C = 20% of 5k = k. Swiggy orders in C = 3k + 20. Since total orders delivered in A = 150, Zomato orders in A = 150 - 5k.

Equating the sum of Zomato orders to 130: (150 - 5k) + 3k + k = 130 150 - k = 130 k = 20

Calculating the required values: Swiggy orders in B = Zomato orders in A = 150 - 5(20) = 50. Zomato orders in C = 20. Swiggy orders in C = 3(20) + 20 = 80. Total orders in C = 20 + 80 = 100.

Required percentage = (50 / 100) × 100 = 50%.

Explanation

Total orders delivered by Zomato in cities A, B, and C = 3 × 43 ⅓ = 130.

Let Swiggy in A = 5x and Zomato in B = 3x. Zomato in C = 20% of 5x = x. Total orders in A (Zomato + Swiggy) = 150, so Zomato in A = 150 - 5x.

Sum of Zomato orders: (150 - 5x) + 3x + x = 130 150 - x = 130 x = 20

Thus: Zomato in A = 150 - 5(20) = 50 Zomato in B = 3(20) = 60 Zomato in C = 20

For city D: Swiggy in D = (Zomato in A + Zomato in C) / 2 = (50 + 20) / 2 = 35 Total orders in D = 90% more than Zomato in B = 60 × 1.90 = 114 Zomato in D = Total orders in D - Swiggy in D = 114 - 35 = 79

Explanation

Total orders delivered by Zomato in A, B, and C = 3 × (43 ⅓) = 130.

Let the number of orders delivered by Swiggy in A and Zomato in B be 5x and 3x respectively. Orders by Zomato in C = 20% of 5x = x. Orders by Zomato in A = 150 - Swiggy in A = 150 - 5x. Orders by Swiggy in B = Zomato in A = 150 - 5x. Orders by Swiggy in C = 3x + 20.

From total Zomato orders: (150 - 5x) + 3x + x = 130 150 - x = 130 x = 20

Thus: Swiggy in C = 3(20) + 20 = 80 Swiggy in B = 150 - 5(20) = 50

For city F: Zomato in F = 80 × (1 - 0.25) = 60 Swiggy in F = 50 - 15 = 35 Total orders in F = 60 + 35 = 95

Explanation

Total orders delivered by Zomato across all three cities = 3 × 43 1/3 = 130.

Let Swiggy in A (S_A) = 5x and Zomato in B (Z_B) = 3x. Zomato in C (Z_C) = 20% of 5x = x. Swiggy in C (S_C) = 3x + 20. Zomato in A (Z_A) = 150 - S_A = 150 - 5x. Swiggy in B (S_B) = Z_A = 150 - 5x.

Using total Zomato orders: Z_A + Z_B + Z_C = 130 (150 - 5x) + 3x + x = 130 150 - x = 130 x = 20

Now compute the total orders in cities B and C: City B total = Z_B + S_B = 3(20) + (150 - 5 × 20) = 60 + 50 = 110. City C total = Z_C + S_C = 20 + (3 × 20 + 20) = 20 + 80 = 100.

Average orders in B and C = (110 + 100) / 2 = 105.

Explanation

Number of non-graduate people in town A = 400 - 290 = 110 Number of non-graduate people in town D = 360 - 245 = 115 Total non-graduates in A and D together = 110 + 115 = 225

Total people in town E = 550 Ratio of males to females in town E = 6 : 5 Number of females in town E = (5 / (6 + 5)) × 550 = (5 / 11) × 550 = 250

Required difference = 250 - 225 = 25

Explanation

Total non-graduates in town C = Total people in C - Graduates in C = 180 - 120 = 60

Males in town D = 360 × 11/(11 + 7) = 360 × 11/18 = 220 Males in town E = 550 × 6/(6 + 5) = 550 × 6/11 = 300

Difference between males in D and E = 300 - 220 = 80

Required percentage = (60 / 80) × 100 = 75%

Explanation

In Town A: Total population = 400 Ratio of Males to Females = 3 : 5 Total males = (3/8) × 400 = 150 Total graduates = 290

Graduate males = 40% of 290 = 116 Graduate females = 290 - 116 = 174 Non-graduate males = Total males - Graduate males = 150 - 116 = 34

Required difference = Graduate females - Non-graduate males = 174 - 34 = 140

Explanation

Total people in F = 60% of 250 = 150.

Number of females in C = (4 / 9) × 180 = 80. Number of females in F = 80 × (1 - 0.40) = 48. Number of males in F = Total in F - Females in F = 150 - 48 = 102.

Number of males in D = (11 / 18) × 360 = 220.

Average number of males in F and D = (102 + 220) / 2 = 322 / 2 = 161.

Explanation

Town B: total=250, M:F=11:14 (25 parts, 10 each) => Males=110, Females=140. Graduates=130, so non-graduates=120. Non-grad M:F=7:5 (12 parts,10 each) => non-grad males=70. Male graduates in B = 110-70=40. 40/400 (total in A) *100 = 10%.

Explanation

Calculate the number of females in towns A, D, and E: Females in A = (5/8) × 400 = 250 Females in D = (7/18) × 360 = 140 Females in E = (5/11) × 550 = 250 Total females in A, D, and E = 250 + 140 + 250 = 640

Calculate the number of non-graduates in towns B and C: Non-graduates in B = 250 - 130 = 120 Non-graduates in C = 180 - 120 = 60 Total non-graduates in B and C = 120 + 60 = 180

Required ratio = 640 : 180 = 32 : 9

Explanation

Initial mixture volume is 180 L with milk and water in the ratio 5:1.

When 40% of the mixture is removed, 60% remains: Remaining mixture = 0.60 × 180 = 108 L

Quantity of milk in remaining mixture = (5/6) × 108 = 90 L Quantity of water in remaining mixture = (1/6) × 108 = 18 L

After adding x liters of pure milk, the ratio of milk to water becomes 7:1: (90 + x) / 18 = 7 / 1 90 + x = 126 x = 126 - 90 = 36

Explanation

Speed of train A = 90 × (5/18) = 25 m/s. Speed of train B = 25 × 1.40 = 35 m/s.

When both trains cross each other in opposite directions, relative speed = 25 + 35 = 60 m/s. Total distance covered = (x + 10) + (x + 20) = 2x + 30 meters. Using Distance = Speed × Time: 2x + 30 = 60 × (11/2) 2x + 30 = 330 2x = 300 x = 150 meters.

Length of train B = 150 + 20 = 170 meters. Total distance to cross the platform = Length of train B + Length of platform = 170 + 110 = 280 meters.

Time taken = Distance / Speed of train B = 280 / 35 = 8 seconds.

Explanation

Total Simple Interest = (P × R₁ × T₁) / 100 + (P × R₂ × T₂) / 100 + (P × R₃ × T₃) / 100

For a total period of 15 years: First 4 years at 8% = 4 × 8% = 32% Next 6 years at 10% = 6 × 10% = 60% Remaining 5 years (15 - 10) at 12% = 5 × 12% = 60%

Total interest percentage = 32% + 60% + 60% = 152% of Principal (P)

152% of P = Rs. 12160 P = (12160 × 100) / 152 = Rs. 8000

Explanation

Amit:Manish=3:2 => 3x,2x. Five yrs ago: 3x-5=2(2x-5) => x=5, so Amit=15, Manish=10. Five yrs hence: Amit=20, Manish=15, sum=35=Lalit's age then. Present age Lalit=35-5=30.

Explanation

Let the length of the rectangle be L cm. Area of rectangle = Length × Breadth = 18L Area of right-angled triangle = ½ × Base × Height = ½(L + 8)(L + 3)

Equating the two areas: 18L = ½(L + 8)(L + 3) 36L = L² + 11L + 24 L² - 25L + 24 = 0 (L - 24)(L - 1) = 0

Since length > breadth (L > 18), L = 24 cm.

Explanation

Let the length of the train be L and its speed be v.

From Statement I: Crossing a tree in 5 seconds gives: L = 5v Crossing a 100 m platform in 10 seconds gives: L + 100 = 10v Substituting L = 5v gives: 5v + 100 = 10v, which yields 5v = 100, so v = 20 m/s. Thus, Statement I alone is sufficient.

From Statement II: When crossing an identical train of length L moving in the opposite direction at the same speed v, the relative speed is 2v and the total distance is 2L. Time = 2L / (2v) = L / v = 20 seconds. This only gives L = 20v, leaving v undetermined. Thus, Statement II alone is not sufficient.

Explanation

From statement I, the rate of B is 1/10 tank/min, and 4 × (rate of A) = 8 × (rate of C), which gives the ratio of rates as rate(A) : rate(C) = 2 : 1. Since absolute rates for A and C cannot be determined, statement I alone is not sufficient.

From statement II, the filling rate of A is 1/10 per min and the rate of B is 1/12 per min. The combined rate of B and C is 1/6 per min, giving the rate of C as 1/6 - 1/12 = 1/12 per min. Therefore, the combined rate of A, B, and C is 1/10 + 1/12 + 1/12 = 1/10 + 1/6 = 4/15 per min, and the tank will be filled in 15/4 = 3.75 min. Statement II alone is sufficient.

Explanation

Probability of drawing 2 red balls is given by P = ᴿC₂ / ᴺC₂, where N is the total number of balls and R is the number of red balls.

From Statement I, total balls N = 10, green balls = 3, and pink balls = 3 − 1 = 2. However, the number of red balls remains unknown, making Statement I alone insufficient.

From Statement II, the relation R = Pink + 2 is given, but without the absolute number of pink balls or total balls, Statement II alone is insufficient.

Combining both statements gives Pink = 2, which yields Red = 2 + 2 = 4. With R = 4 and N = 10, P = ⁴C₂ / ¹⁰C₂ = 6 / 45 = 2/15. Thus, both statements together are necessary and sufficient.

Explanation

Approximate each term to its nearest convenient integer: 189.98 ≈ 190 49.96% ≈ 50% = ½ 539.98 ≈ 540 630.03 ≈ 630

Substitute these approximations into the given equation: 190 + (50% of 540) + ? = 630 190 + 270 + ? = 630 460 + ? = 630 ? = 630 - 460 = 170

Explanation

(276.02/12.03)(79.99/115.01)? = 31.99% of 199.98. Approx: (276/12)(80/115)? ≈ 230.696? ≈16*? ... more precisely 23*0.6955=16.0; RHS≈32%*200=64. ?=64/16≈4.

Explanation

Approximate each value to its nearest integer: 184.001 ÷ 3.997 ≈ 184 ÷ 4 = 46

Numerator = 284.02 + 46 = 330 Denominator = 594.01 ÷ 9.02 ≈ 594 ÷ 9 = 66

Value of the expression = 330 ÷ 66 = 5

Explanation

Approximating each term to the nearest whole number: 684.03 ≈ 684 2171.999 ÷ 5.98 ≈ 2172 ÷ 6 = 362 49.98 × 5.02 ≈ 50 × 5 = 250

Summing the terms: 684 + 362 + 250 = 1296

Solving for ?: ?² = 1296 ? = √1296 = 36

Explanation

Approximate the given values to the nearest whole numbers: 79.97% ≈ 80% 250.02 ≈ 250 4.99 ≈ 5 4.97 ≈ 5

Substitute these into the expression: (80% of 250) of 5 ÷ 5² = ((80 / 100) × 250) of 5 ÷ 25 = 200 of 5 ÷ 25 = (200 × 5) ÷ 25 = 1000 ÷ 25 = 40

Explanation

Approximating the numbers to their nearest convenient values: 24.89% of 624.09 ≈ 25% of 624 = 156 19.7% of 994.89 ≈ 20% of 995 ≈ 196 397.97 ≈ 398 19.78 ≈ 20 19.14 × 23.06 ≈ 19.1 × 23.1 ≈ 441

Substituting these values into the expression: (156 / 196) × 398 - 20 = ?³ - 441 (156 × 2) - 20 ≈ ?³ - 441 312 - 20 = ?³ - 441 296 = ?³ - 441 ?³ = 296 + 441 = 737

Since 9³ = 729, the value of ? is 9.

Explanation

The series follows the recurrence relation Tₙ = 2 × Tₙ₋₁ + 1:

17 × 2 + 1 = 35 35 × 2 + 1 = 71 71 × 2 + 1 = 143 143 × 2 + 1 = 287 287 × 2 + 1 = 575 575 × 2 + 1 = 1151

Each successive term is obtained by multiplying the previous term by 2 and adding 1. Applying this pattern to 575 yields 1151, which makes 1150 the incorrect term in the sequence.

Explanation

The pattern of multiplication between consecutive terms is: 128 × 0.5 = 64 64 × 1.5 = 96 96 × 2.5 = 240 240 × 3.5 = 840 840 × 4.5 = 3780 3780 × 5.5 = 20790

The multiplier increases by 1.0 at each step (0.5, 1.5, 2.5, 3.5, 4.5, 5.5). Therefore, 32 is incorrect and should be replaced by 64.

Explanation

Series follows term(n+2)=average(term n, term n+1): (91+235)/2=163 ✓, (235+163)/2=199 ✓, (163+199)/2=181 ✓, (199+181)/2=190 ✓, but (181+190)/2=185.5, not the printed 187.5. So 187.5 is the wrong number.

Explanation

The series follows a pattern of alternating second differences: 75 - 15 = 60 129 - 75 = 54 (second difference: -6) 191 - 129 = 62 (second difference: +8) 243 - 191 = 52 (second difference: -10)

The sequence of second differences is -6, +8, -10, +12, -14. Applying the next second difference (+12): Required difference = 52 + 12 = 64 Correct term = 243 + 64 = 307

Applying the final second difference (-14): Final difference = 64 - 14 = 50 Final term = 307 + 50 = 357

Replacing 309 with 307 satisfies the series progression.

Explanation

The differences between consecutive terms follow an arithmetic progression with a constant step of 9: 388 - 313 = 75 313 - 247 = 66 247 - 190 = 57 The preceding differences must therefore be 57 - 9 = 48 and 48 - 9 = 39.

Calculating forward from the first term: 103 + 39 = 142 142 + 48 = 190 190 + 57 = 247 247 + 66 = 313 313 + 75 = 388

The term 145 disrupts the pattern and should be replaced by 142.

Explanation

The differences between consecutive terms in the series follow a sequence of consecutive prime numbers: 473 − 67 = 406 406 − 71 = 335 335 − 73 = 262 262 − 79 = 183 183 − 83 = 100 100 − 89 = 11

Replacing 99 with 100 correctly satisfies the pattern of subtracting consecutive prime numbers (67, 71, 73, 79, 83, 89).