IBPS Clerk Prelims 2023 Question Paper with Answers & Explanations

Explanation

The chronological order of the eight birth dates across the four months is April 5, April 20, May 5, May 20, July 5, July 20, September 5, and September 20.

F is born on an odd date in a month with an odd number of days (May 5, which has 31 days) immediately before H (May 20). Since 5 persons are born after F, 5 persons must be born before D, placing D on July 20. A is born on July 5, placing G two persons after A on September 5, and E immediately after G on September 20. C is born before B, placing C on April 5 and B on April 20.

The complete schedule from earliest to latest is: April 5: C April 20: B May 5: F May 20: H July 5: A July 20: D September 5: G September 20: E

There are 2 persons (A and D) born between G and H. Similarly, there are 2 persons (C and B) born before F. Thus, the number of persons born between G and H is the same as the number of persons born before F.

Explanation

The eight birth dates in chronological order are April 5, April 20, May 5, May 20, July 5, July 20, September 5, and September 20. F was born on an odd date (5th) in a month with 31 days (May or July) immediately before H. If F is born on May 5, H is born on May 20. Since the number of persons born after F equals the number born before D, D is born on July 20. G was born two persons after A, and E was born immediately after G, which means A, gap, G, E form a sequence. Placing A on July 5 gives G on September 5 and E on September 20. The remaining persons C and B occupy April 5 and April 20 respectively, satisfying C being born before B. Thus, E was born in September.

Explanation

The chronological order of the eight birth dates is April 5, April 20, May 5, May 20, July 5, July 20, September 5, and September 20.

F was born on an odd date (5th) in a month with 31 days (May) directly before H, placing F on May 5 and H on May 20.

Since 5 persons were born after F, exactly 5 persons were born before D, placing D on July 20.

G was born two positions after A, and E was born immediately after G. This sequence fits by placing A on July 5, G on September 5, and E on September 20.

The remaining open dates, April 5 and April 20, are occupied by C and B respectively, as C was born before B.

The complete order from earliest to latest is: C (April 5), B (April 20), F (May 5), H (May 20), A (July 5), D (July 20), G (September 5), and E (September 20).

Since A was born on July 5, exactly three persons (D, G, and E) were born after A.

Explanation

The chronological order of birth dates is April 5, April 20, May 5, May 20, July 5, July 20, September 5, and September 20.

F was born on May 5 (an odd date in a 31-day month) immediately before H, who was born on May 20. Since 5 persons were born after F, exactly 5 persons were born before D, placing D on July 20.

A was born on July 5, placing G two persons later on September 5, followed immediately by E on September 20. C was born before B, placing C on April 5 and B on April 20.

The complete sequence from earliest to latest is C, B, F, H, A, D, G, E. Both F and H were born in May, making H born in the month of May.

Explanation

Arranging the eight birth dates chronologically gives eight positions: April 5, April 20, May 5, May 20, July 5, July 20, September 5, and September 20.

Since F was born on an odd date in a month with 31 days (odd days) immediately before H, F was born on May 5 and H on May 20. Exactly five persons were born after F, so five persons must be born before D, placing D on July 20.

Next, G was born two persons after A, and E was born immediately after G. This sequence fits only when A is placed on July 5, G on September 5, and E on September 20.

Finally, since C was born before B, they fill the remaining vacant slots with C on April 5 and B on April 20.

Comparing their birth dates, B was born on April 20 and D was born on July 20, confirming that D was born after B.

Explanation

The phrase "Only a few birds are mammal" implies that while some birds are mammals, some birds are definitely not mammals. Because a section of birds can never be included in mammals, all birds can never be mammals, making Conclusion I definitely true.

Additionally, since a portion of birds consists of mammals, and no mammal is carnival, that specific portion of birds can never be carnival. This proves that some birds are not carnival, making Conclusion II definitely true. Consequently, both conclusions logically follow from the given statements.

Explanation

Since all symbols are letters and no letter is a ruin, no symbol can ever be a ruin. Therefore, it is impossible for all symbols to be a ruin, so Conclusion I does not follow.

Statement 1 establishes that some numbers are letters. Because no letter is a ruin, the specific numbers that are letters can never be a ruin. This directly proves that some numbers are not ruin, making Conclusion II logically follow.

Explanation

Placing F at position 1 in a 1 to 8 clockwise arrangement facing the centre, E sits second to the right at position 3. Since two persons sit between A and E, placing A at position 8 leaves room for B and G at opposite positions 6 and 2, which puts C at position 4 so that B is second to C's right. With A at position 8, H cannot sit at position 7 adjacent to A, placing H at position 5 and D at position 7.

The resulting clockwise sequence from positions 1 to 8 is F, G, E, C, H, B, D, A.

Counting counter-clockwise (to the left) from H at position 5 to G at position 2 passes through C (position 4) and E (position 3), giving a total of two persons between them.

Explanation

In a circular seating arrangement of eight persons facing the centre, two persons who face each other are positioned directly opposite one another. On an eight-person table, opposite positions are separated by exactly three seats along both the clockwise and counter-clockwise directions. Since B directly faces G as stated in the arrangement, there are exactly three persons sitting between B and G.

Explanation

By placing the eight persons around the circular table facing the centre according to the given clues, the unique valid clockwise seating arrangement starting from A is:

A, D, B, H, C, E, G, F

When all eight persons sit in alphabetical order starting from A in a clockwise direction, the new arrangement becomes:

A, B, C, D, E, F, G, H

Comparing the positions relative to A (excluding A): Position 2: D in original, B in new Position 3: B in original, C in new Position 4: H in original, D in new Position 5: C in original, E in new Position 6: E in original, F in new Position 7: G in original, G in new Position 8: F in original, H in new

Only G retains the same position (7th spot relative to A) in both arrangements. Thus, the position of only one person remains unchanged.

Explanation

Placing all eight persons around the circular table facing the centre:

If F is placed at position 1, then E, sitting second to the right of F, is at position 7.

With two persons between A and E along the counter-clockwise direction, A is at position 2.

Since B faces G, the opposite pair of available seats is at positions 4 and 8. Placing C at position 6 means B sits second to the right of C at position 4, leaving G at position 8.

Since H cannot sit adjacent to A at position 3, H occupies position 5.

Thus, D occupies the remaining position 3.

Moving clockwise (to the left) from F at position 1, position 2 is A and position 3 is D. Therefore, D sits second to the left of F.

Explanation

By determining the positions of the eight persons facing the centre around the circular table, the clockwise seating order is F, A, D, B, H, C, E, and G. In this arrangement, persons sitting directly opposite each other form pairs: F and H, A and C, D and E, and B and G. The pair B-A does not consist of opposite-facing persons, as B and A sit with D between them. Therefore, B-A is the odd pair that does not belong to the group.

Explanation

D is married to G's daughter, making their child K the grandchild of G. Thus, G is the maternal grandmother of K. F is the brother of G. Since F is the brother-in-law of H, H must be married to F's sister G. Therefore, H is the husband of G, which makes H the grandfather of K.

Explanation

From the given information, G's daughter is married to D, and M is the sister-in-law of B, who is D's sibling. This confirms that M is the daughter of G and is married to D. Since F is the only brother of G, F is the brother of M's mother. Therefore, F is the maternal uncle of M.

Explanation

A is the mother of D and B. G's daughter is married to D, which means D is male and his wife is G's daughter. Since M is the sister-in-law of B and vice versa, M is D's wife (and G's daughter).

G is the grandmother of K, which makes K the child of the married couple D and M. Since D is the father of K, any person C who is married to K (as his wife) makes D her husband's father. Therefore, D is the father-in-law of C.

Explanation

When finding an element located to the right of another element measured from the right end, subtract the positions:

Net position from the right end = 11 - 6 = 5th element from the right end.

Counting backwards from the right end of the given series: 1st from right: Z 2nd from right: D 3rd from right: π 4th from right: S 5th from right: Φ

Thus, the required element is Φ.

Explanation

Removing all symbols from the given series leaves only the alphabetic characters in their original relative order: Q, W, E, S, R, T, Y, Q, B, H, I, O, Y, P, L, O, K, J, U, M, G, F, A, S, D, Z. Counting sequentially from the left end, the first eight letters are Q (1st), W (2nd), E (3rd), S (4th), R (5th), T (6th), Y (7th), and Q (8th).

Explanation

In the given series, a vowel must be immediately preceded by a letter and immediately followed by a symbol. Examining all the vowels in the series: E is preceded by @ (symbol); I is followed by O (letter); O is followed by Y (letter); O is followed by K (letter); U is followed by M (letter); A is preceded by F (letter) and followed by Φ (symbol). Thus, only one vowel (A) satisfies the required condition.

Explanation

In the given alphabet and symbol series, four of the groups follow a consistent positional pattern: starting from the first character at position n, the second character is two steps to the right (position n + 2), and the third character is one step to the left (position n - 1).

For example, in WE!, E is two steps to the right of W and ! is one step to the left of W. Similarly, in %&R, & is two steps to the right of % and R is one step to the left of %. In ASF, S is two steps to the right of A and F is one step to the left of A.

However, H βO consists of characters located in consecutive positions (n, n + 1, n + 2) in the series rather than following the (+2, -1) positional rule, making it the odd one out.

Explanation

Counting the letters from the right end of the given series in order: Z (1st), D (2nd), S (3rd), A (4th), F (5th), G (6th), M (7th), and U (8th). To the right of U, the symbols present in the series are α, Φ, and π. Thus, there are 3 symbols to the right of the 8th letter from the right end.

Explanation

In the given number 38172946, a pair of digits has as many digits between them as in the natural number series when the difference between their position indices equals the absolute difference between their values.

Scanning in the forward direction (left to right): The pair 1 and 6 (at positions 3 and 8) has a position difference of 5 and a digit difference of 5 (6 - 1 = 5). The pair 7 and 9 (at positions 4 and 6) has a position difference of 2 and a digit difference of 2 (9 - 7 = 2). The pair 2 and 4 (at positions 5 and 7) has a position difference of 2 and a digit difference of 2 (4 - 2 = 2).

Scanning in the backward direction (right to left): The pair 3 and 1 (at positions 1 and 3) has a position difference of 2 and a digit difference of 2 (3 - 1 = 2). The pair 7 and 4 (at positions 4 and 7) has a position difference of 3 and a digit difference of 3 (7 - 4 = 3).

In total, there are 5 such pairs (1-6, 7-9, 2-4, 3-1, and 7-4), which is more than four.

Explanation

Arranging the seven persons day-wise from Monday to Sunday:

Since at most one person goes before C and an equal number of persons go before C as after E, C goes on Monday and E goes on Sunday.

With two persons between E and D, D is placed on Thursday.

G goes two persons after A, which places A on Wednesday and G on Friday.

Since more than two persons go between F and B, and A goes before B, F goes on Tuesday and B goes on Saturday.

The complete schedule from Monday to Sunday is C, F, A, D, G, B, and E. Therefore, D goes to watch the movie on Thursday.

Explanation

Arranging the seven persons on days from Monday to Sunday:

Since at most one person goes before C and as many go before C as after E, C goes on Monday (0 before C) and E goes on Sunday (0 after E).

Two persons go between E and D, placing D on Thursday.

G goes two persons after A, which means A is followed by one person and then G. The only available days that fit this pattern are Wednesday for A and Friday for G.

The remaining days for F and B are Tuesday and Saturday. Since more than two persons go between F and B, they must occupy Tuesday and Saturday. Given that A does not go after B, B is on Saturday and F is on Tuesday.

The complete schedule from Monday to Sunday is: C, F, A, D, G, B, E.

The four persons who go to watch the movie between C (Monday) and B (Saturday) are F, A, D, and G.

Explanation

Assigning the days from Monday to Sunday in sequence from 1 to 7:

Since at most one person goes before C and the number of persons before C equals the number after E, C must be on Monday and E on Sunday. Two persons between E and D places D on Thursday.

G goes two persons after A, which means A is on Wednesday and G is on Friday. The remaining available days are Tuesday and Saturday for F and B. Since more than two persons go between F and B, F is on Tuesday and B is on Saturday. This also satisfies that A (Wednesday) does not go after B (Saturday).

Thus, B goes to watch the movie on Saturday.

Explanation

By evaluating the given conditions, the unique schedule from Monday to Sunday is determined as follows:

C goes on Monday, making E go on Sunday so that the number of persons before C equals the number after E. D goes on Thursday, leaving two days between D and E. A goes on Wednesday and G goes on Friday, satisfying G going two persons after A. To keep more than two persons between F and B with A before B, F must go on Tuesday and B on Saturday.

Thus, the complete schedule from Monday to Sunday is C, F, A, D, G, B, E. Since C goes to watch the movie on Monday and F goes on Tuesday, the statement that F goes on Monday is false.

Explanation

Based on the given conditions, the schedule from Monday to Sunday is determined as follows:

Placing C on Monday leaves zero persons before C, which means zero persons go after E, placing E on Sunday. Two persons between E and D places D on Thursday. Since G goes two persons after A, A is on Wednesday and G is on Friday. Since A goes before B and more than two persons go between F and B, F is on Tuesday and B is on Saturday.

The original schedule from Monday to Sunday is: C, F, A, D, G, B, E.

Arranging the persons in alphabetical order from Monday to Sunday gives: A, B, C, D, E, F, G.

Comparing the two arrangements, only D remains in the same position on Thursday, while the positions of the remaining six persons (C, F, A, G, B, E) changed.

Explanation

The specified letters extracted from the word FRANCHISE are: 1st letter: F 2nd letter: R 4th letter: N 6th letter: H

Using the letters F, R, N, and H, no meaningful four-letter English word can be formed. According to the given instructions, when no meaningful word can be formed, the answer is designated as X.

Explanation

Arranging the six persons in descending order of height from position 1 (tallest) to position 6 (shortest):

The condition that only one person is shorter than T directly places T at position 5, which means T is the second shortest person.

To complete the order: since S is shorter than U, S must occupy position 6 (shortest). This leaves two persons (T and S) shorter than U, placing U at position 4. Since the number of persons taller than P equals the number shorter than U (two persons), P is at position 3. R is taller than U and shorter than Q, placing R at position 2 and Q at position 1.

The final order from tallest to shortest is Q > R > P > U > T > S, where T is the second shortest person.

Explanation

Arranging the six persons in descending order of height from position 1 (tallest) to position 6 (shortest):

Since only one person is shorter than T, T is at position 5. S is shorter than U, placing S at position 6.

With T and S at positions 5 and 6, exactly 2 persons are shorter than U, placing U at position 4. The number of persons taller than P equals the number of persons shorter than U, so 2 persons are taller than P, placing P at position 3.

Q and R occupy positions 1 and 2. Since R is shorter than Q, Q is at position 1 and R is at position 2.

The complete height order from tallest to shortest is Q > R > P > U > T > S. Exactly three persons (Q, R, and P) are taller than U.

Explanation

Arranging the six persons from 1 (tallest) to 6 (shortest):

Only one person is shorter than T, which places T at position 5. Since S is shorter than U, S takes position 6.

With U at position 4, exactly two persons (T and S) are shorter than U. To satisfy the condition that as many persons are taller than P as shorter than U, two persons must be taller than P, placing P at position 3.

The remaining positions 1 and 2 belong to Q and R. Since R is taller than U but shorter than Q, Q is at position 1 and R is at position 2.

The final height order from tallest to shortest is Q > R > P > U > T > S.

Given that R is 154 cm, Q is taller than R and must have a height greater than 154 cm. The only possible height strictly greater than 154 cm is 158 cm.

Explanation

Comparing the first statement with the others:

Comparing "Dream your special wish" (mr kt wc sg) with "Your willing is dream" (lg ut wc kt) gives common words "dream" and "your" matching codes "wc" and "kt".

Comparing "Dream your special wish" with "Special dream is aim" (wc qk mr lg) and "Think wise special willing" (yl ut mr pt) shows that "special" is present in all three, matching the common code "mr".

Thus, in the first statement, "dream" is "wc", "your" is "kt", and "special" is "mr". The remaining word "wish" corresponds directly to the remaining code "sg".

Explanation

Comparing statements 1, 2, and 3 shows that "dream" is coded as "wc". Comparing statements 1, 3, and 4 shows that "special" is coded as "mr". Comparing statements 2 and 4 shows that "willing" is coded as "ut".

In the fourth statement, "Think wise special willing" corresponds to "yl ut mr pt". Substituting the established codes for "special" (mr) and "willing" (ut), the remaining words "Think" and "wise" correspond to the remaining codes "yl" and "pt". Because neither word appears in any other statement, "pt" cannot be uniquely assigned and thus represents either "think" or "wise".

Explanation

Comparing the statements to decode common words gives: special = mr willing = ut

In the fourth statement, "Think wise special willing" is coded as "yl ut mr pt". Substituting the known codes for "special" and "willing" leaves "think" and "wise" as "yl" and "pt" in some order.

Since "think twice" is given as "dw yl", the common word "think" corresponds to "yl", which means "wise" is coded as "pt".

For "wise towards", the code for "wise" must be "pt", and "towards" (being a new word not present in any given statement) must take a new code not appearing in the original statements. Among the given choices, "vx" is a completely new code word, making "pt vx" the correct code for "wise towards".

Explanation

By comparing common words across the sentences:

"dream" appears in sentences 1, 2, and 3, where the only common code is "wc", so "dream" = "wc".

In sentence 4, "special" is coded as "mr" (common in sentences 1, 3, and 4) and "willing" is coded as "ut" (common in sentences 2 and 4). This leaves the words "Think" and "wise" paired with the remaining codes "yl" and "pt". Therefore, "wise" can be coded as either "pt" or "yl".

Combining these, the code for "Dream wise" is either "pt wc" or "wc yl".

Explanation

Comparing the given coded sentences: From sentences 1 and 3, special and dream correspond to mr and wc. From sentences 1 and 2, dream and your correspond to wc and kt. Comparing these gives dream = wc, special = mr, and your = kt. From sentence 3, since special = mr and dream = wc, the remaining words aim and is are coded by qk and lg. Comparing sentences 2 and 3 shows is = lg, which leaves aim = qk. Therefore, mr qk is the code for special aim or aim special.

Explanation

The given pattern consists of two alternating sub-series, where each term increases by 43:

First sub-series (1st, 3rd, 5th, and 7th terms): 91 + 43 = 134 134 + 43 = 177 177 + 43 = 220

Second sub-series (2nd, 4th, and 6th terms): 164 + 43 = 207 207 + 43 = 250

Alternatively, consecutive terms follow the alternating arithmetic pattern (+73, -30): 91 + 73 = 164 164 - 30 = 134 134 + 73 = 207 207 - 30 = 177 177 + 73 = 250 250 - 30 = 220

Therefore, 245 is the wrong number in the series and should be replaced with 250.

Explanation

The pattern of the series from right to left is: 1234 = 1233 × 1 + 1 1233 = 616 × 2 + 1 616 = 205 × 3 + 1 205 = 51 × 4 + 1 Following this rule, the term preceding 51 should be (51 - 1) / 5 = 10. Checking the first term: 10 × 6 + 1 = 61, or 1.5 × 6 + 1 = 10. Thus, 9 is wrong and should be replaced by 10.

Explanation

The series follows the pattern from right to left where each term is calculated as: Next term = (Current term × 2) - 28

Calculating from right to left: 46 × 2 - 28 = 64 64 × 2 - 28 = 100 100 × 2 - 28 = 172 172 × 2 - 28 = 316 316 × 2 - 28 = 604 604 × 2 - 28 = 1180

Alternatively, the differences between consecutive terms from right to left double at each step: +18, +36, +72, +144, +288, +576.

Since 316 + 288 = 604 and 604 + 576 = 1180, the term 600 is incorrect and should be replaced by 604.

Explanation

The pattern in the series is based on adding increments that increase by 1 at each step:

15.5 + 3.5 = 19 19 + 4.5 = 23.5 23.5 + 5.5 = 29 29 + 6.5 = 35.5 35.5 + 7.5 = 43 43 + 8.5 = 51.5

The consecutive differences follow the sequence 3.5, 4.5, 5.5, 6.5, 7.5, and 8.5. Adding 7.5 to 35.5 gives 43, which when added to 8.5 correctly yields the final term 51.5. Thus, 40 breaks the pattern and should be replaced by 43.

Explanation

The pattern in the series is formed by adding decreasing squares of consecutive even numbers:

23 + 18² = 23 + 324 = 347 347 + 16² = 347 + 256 = 603 603 + 14² = 603 + 196 = 799 799 + 12² = 799 + 144 = 943 943 + 10² = 943 + 100 = 1043 1043 + 8² = 1043 + 64 = 1107

The number 940 violates this pattern and should be replaced by 943.

Explanation

Bikes manufactured by A in 2021 = 120. Bikes manufactured by B and C together in 2022 = 320 + 300 = 620. Required ratio = 120 : 620 = 6 : 31.

Explanation

Total bikes manufactured by company D in 2021 = 260.

Brand X bikes comprise 30% of the total, so brand Y bikes account for the remaining 70%.

The difference in percentage between brand Y and brand X bikes = 70% - 30% = 40%.

Required difference = 40% of 260 = (40 / 100) × 260 = 104.

Explanation

Total revenue generated by company C is the sum of the revenues earned in the years 2021 and 2022.

Revenue in 2021 = Number of bikes manufactured in 2021 × Selling price per bike Revenue in 2021 = 240 × 8000 = Rs. 19,20,000

Revenue in 2022 = Number of bikes manufactured in 2022 × Selling price per bike Revenue in 2022 = 300 × 9000 = Rs. 27,00,000

Total revenue in both years = 19,20,000 + 27,00,000 = Rs. 46,20,000 (or 4620000 Rs.)

Explanation

Total bikes manufactured by C in 2021 and D in 2022 together = 240 + 240 = 480.

Total bikes manufactured by A and B together in 2021 = 120 + 180 = 300.

Required percentage = (480 ÷ 300) × 100 = 160%.

Explanation

Total bikes manufactured by C, D, and E in 2021 = 290 × 3 = 870. From the table, bikes manufactured by C in 2021 = 240, and by D in 2021 = 260. Total bikes manufactured by C and D in 2021 = 240 + 260 = 500. Bikes manufactured by E in 2021 = 870 - 500 = 370.

Explanation

Let the breadth of the rectangle be B cm and length L = 12 cm. The side of the square S = (12 + B) - 14 = B - 2 cm.

Using the perimeter formulas: Perimeter of rectangle = 2(L + B) = 2(12 + B) = 24 + 2B cm Perimeter of square = 4 × S = 4(B - 2) = 4B - 8 cm

Given that the perimeter of the rectangle is 16 cm more than the perimeter of the square: 24 + 2B = (4B - 8) + 16 24 + 2B = 4B + 8 4B - 2B = 24 - 8 2B = 16 B = 8 cm

Explanation

Weight of new person = New total weight - Initial total weight

Initial total weight = 5 × 85 = 425 kg New average weight = 85 - 5 = 80 kg New total weight for 6 people = 6 × 80 = 480 kg

Weight of new person = 480 kg - 425 kg = 55 kg

Alternatively, using the direct formula for a new entry: Weight of new person = New Average + (Old Count × Change in Average) Weight of new person = 80 + 5 × (-5) = 80 - 25 = 55 kg

Explanation

Time taken by A and B together to complete the total work = 3 × 4 = 12 days. A's 1-day rate of work = 1/40, and (A + B)'s combined 1-day rate of work = 1/12.

Work completed by A alone in the first 8 days = 8 × (1/40) = 1/5. Remaining work = 1 - (1/5) = 4/5.

Time taken by A and B together to finish the remaining work = (Remaining Work) / (Combined 1-day rate) = (4/5) / (1/12) = (4 × 12) / 5 = 48/5 = 9.6 days.

Explanation

Profit ratio equals the product of investment and time duration.

A invested Rs. 8000 for 12 months, giving an equivalent investment product of 8000 × 12 = 96000. B invested Rs. X for 6 months, giving an equivalent investment product of X × 6 = 6X.

Total profit is Rs. 49000 and B's share is Rs. 21000, so A's share is 49000 - 21000 = Rs. 28000.

Ratio of A's share to B's share: 28000 / 21000 = 96000 / 6X 4 / 3 = 16000 / X 4X = 48000 X = 12000

Explanation

First selling price = Cost Price × 1.40 × (1 - 0.20) = 1.12 × Cost Price. Second selling price = Cost Price × 1.50 × (1 - 0.12) = 1.32 × Cost Price. Difference in selling price = 1.32 × Cost Price - 1.12 × Cost Price = 0.20 × Cost Price. Given 0.20 × Cost Price = 90, so Cost Price = 450. 130% of Cost Price = 1.30 × 450 = 585.

Explanation

Upstream speed = Distance / Time = 54 / 9 = 6 km/h Downstream speed = Distance / Time = 60 / 5 = 12 km/h

Speed of boat in still water = (Downstream speed + Upstream speed) / 2 = (12 + 6) / 2 = 9 km/h Speed of stream = (Downstream speed − Upstream speed) / 2 = (12 − 6) / 2 = 3 km/h

Ratio of speed of boat in still water to speed of stream = 9 : 3 = 3 : 1.

Explanation

Let the present age of B be b years.

After x years, A's age is 26 + x and B's age is b + x. (26 + x) / (b + x) = 7 / 5 5(26 + x) = 7(b + x) 2x + 7b = 130 --- Equation (1)

After (x + 4) years, A's age is 30 + x and B's age is b + x + 4. (30 + x) / (b + x + 4) = 4 / 3 3(30 + x) = 4(b + x + 4) x + 4b = 74 --- Equation (2)

Multiplying Equation (2) by 2 gives 2x + 8b = 148. Subtracting Equation (1) from this: (2x + 8b) - (2x + 7b) = 148 - 130 b = 18 years.

Explanation

Simple interest formula is SI = (P × R × T) / 100. 1800 = (4000 × R × 3) / 100 120R = 1800 R = 15%

The new rate of interest for compound interest is R - 5% = 15% - 5% = 10% p.a.

For compound interest over 2 years at 10% p.a., the effective percentage rate is 10 + 10 + (10 × 10) / 100 = 21%.

Compound interest received = 21% of 5000 = 0.21 × 5000 = 1050 Rs.

Explanation

Time taken by the train to cross the pole is 1 minute 5 seconds, which equals 65 seconds.

Speed of the train = Length of train / Time taken = 780 / 65 = 12 m/s.

Since the ratio of the speed of the train to that of the man is 6 : 1, the speed of the man = 12 / 6 = 2 m/s.

To cross the 240 m long platform, the time taken by the man = Distance / Speed = 240 / 2 = 120 seconds.

Explanation

Let the initial quantity of milk be M litres. Initial water = 0.40 M litres, so the ratio of water to milk is 2 : 5. In 28 litres of mixture removed: Water removed = (2 / 7) × 28 = 8 litres. Milk removed = (5 / 7) × 28 = 20 litres. After adding 10 litres of water: New water quantity = 0.40 M - 8 + 10 = 0.40 M + 2. New milk quantity = M - 20. Given that new water is 60% of new milk: 0.40 M + 2 = 0.60 × (M - 20) 0.40 M + 2 = 0.60 M - 12 0.20 M = 14 M = 70 litres.

Explanation

Using the order of operations, the expression 895 ÷ 25 × 400 ÷ 20 can be rewritten as a single combined fraction:

? = (895 × 400) / (25 × 20)

Simplifying the denominator: ? = (895 × 400) / 500

Canceling common factors in 400/500 gives 4/5: ? = 895 × (4 / 5) ? = 179 × 4 ? = 716

Explanation

√1225 = 35 40% of 30 = (40/100) × 30 = 12

Left-hand side = 35 × 12 = 420 Right-hand side = ? + (30 × 4) = ? + 120

Equating both sides: 420 = ? + 120 ? = 420 − 120 = 300

Explanation

Let the unknown value be x.

The given equation is: (x / 100) × 625 + 20% of 955 = 21²

Evaluating the known terms: 21² = 441 20% of 955 = 191

Substituting these values into the equation: (x / 100) × 625 + 191 = 441 (x / 100) × 625 = 441 - 191 6.25 × x = 250 x = 250 / 6.25 = 40

Explanation

First, calculate 170% of 500: 170% of 500 = (170 / 100) × 500 = 850

Next, calculate 15²: 15² = 225

Substituting these values into the given equation 5^? + 15² = 170% of 500 gives: 5^? + 225 = 850 5^? = 850 - 225 5^? = 625

Since 625 = 5⁴, we have: 5^? = 5⁴

Comparing the exponents on both sides gives ? = 4.

Explanation

Simplify both sides of the equation:

Left Hand Side: 12 × 15 + 27 = 180 + 27 = 207

Right Hand Side: 28% of 400 = (28 ÷ 100) × 400 = 28 × 4 = 112

Substituting these values into the equation: 207 - ? = 112 ? = 207 - 112 = 95

Explanation

Calculate the percentage terms on both sides of the equation:

First term on the left side: (32 / 100) × 850 = 32 × 8.5 = 272

Term on the right side: (14 / 100) × 640 = 14 × 6.4 = 89.6

Substitute these values back into the original equation: 272 - ? = 89.6

Rearranging the equation to find the value of the missing term (?): ? = 272 - 89.6 ? = 182.4

Explanation

Simplify the given expression by applying the standard order of operations (BODMAS):

Evaluating each division term first: 170 ÷ 34 = 5 25 ÷ 5 = 5 742 ÷ 14 = 53

Next, perform the multiplication for the first part of the expression: 5 × 5 = 25

Finally, add the remaining value to complete the calculation: 25 + 53 = 78

Explanation

To solve the addition of mixed fractions, separate the integer parts and the fractional parts:

Sum of whole numbers = 4 + 3 + 7 = 14

Sum of fractional parts = 2/9 + 1/3 + 1/18

Converting fractions to a common denominator of 18: 2/9 = 4/18 1/3 = 6/18 1/18 = 1/18

Sum of fractions = 4/18 + 6/18 + 1/18 = 11/18

Combining the whole number and fractional sum gives 14 11/18.

Explanation

Given the equation: (626 + 374 - ?) × 3/5 = 81

First, evaluate the addition inside the parenthesis: 626 + 374 = 1000

Substituting this back into the equation gives: (1000 - ?) × 3/5 = 81

Multiply both sides by 5 to clear the fraction: (1000 - ?) × 3 = 81 × 5 (1000 - ?) × 3 = 405

Divide both sides by 3: 1000 - ? = 405 / 3 1000 - ? = 135

Solving for ?: ? = 1000 - 135 ? = 865

Explanation

Given: 400 + (?)² = (28)² + √(256)

Evaluating the values on the right-hand side: (28)² = 784 √(256) = 16

Substituting these into the equation: 400 + (?)² = 784 + 16 400 + (?)² = 800 (?)² = 800 - 400 (?)² = 400 ? = √400 = 20

Explanation

Calculate each component of the given equation:

42% of 800 = (42 / 100) × 800 = 336 19² = 361

Substitute these values back into the equation: 336 + 725 / ? = 361

Subtract 336 from both sides: 725 / ? = 361 - 336 725 / ? = 25

Solving for the missing value: ? = 725 / 25 = 29

Explanation

7.5% of 750 + ?² = 52 × 11 + 109.25 (7.5 / 100) × 750 + ?² = 572 + 109.25 56.25 + ?² = 681.25 ?² = 681.25 - 56.25 = 625 ? = √625 = 25.

Explanation

Following the BODMAS rule, perform division and multiplication from left to right:

First term: (15 × 6) ÷ 0.18 ÷ 5 = 90 ÷ 0.18 ÷ 5 = 500 ÷ 5 = 100

Second term: 5.5 ÷ 1.1 = 5

Adding both terms together: 100 + 5 = 105

Explanation

(1 / 3) × ?⁴ = √121 + 4² (1 / 3) × ?⁴ = 11 + 16 = 27 ?⁴ = 27 × 3 = 81 ? = ∜81 = 3.

Explanation

First, simplify the fraction addition: 14/3 + 31/6 = (28 + 31) / 6 = 59/6

Next, calculate the percentage term: 45% of 240 = (45 / 100) × 240 = 108

Now, multiply the two simplified expressions: ? = (59/6) × 108

Since 108 ÷ 6 = 18, substitute this back: ? = 59 × 18 = 1062

Explanation

The passage explicitly states that the village had been suffering from an ancient salt deficiency for generations. This severe lack of salt rendered the soil too poor to produce healthy crops and caused the villagers to suffer from weakness, sickness, and premature death, directly linking the salt deficiency to both crop failure and health issues.

Explanation

According to the passage, Ato was determined to help his village overcome its ancient salt deficiency. To solve this problem, he travelled far and wide, studied ancient texts, met with wise scholars, and visited distant lands to gain knowledge about salt and its production methods. Upon returning, he shared this knowledge with the villagers and taught them how to build a salt mine, directly addressing the core cause of their poor crops and ill health.

Explanation

According to the passage, when Ato returned and shared his findings about salt, the villagers were initially skeptical. Having never heard of salt before, they doubted that it could solve their long-standing health and crop issues. Their initial disbelief required Ato to be patient and persistent to gradually convince them to adopt his methods.

Explanation

According to the passage, after returning to his village, Ato taught the people how to grow crops that required salt and showed them how to build a salt mine. This directly addressed the ancient salt deficiency that affected the soil, improved crop health, and helped the villagers overcome their weakness and sickliness.

Explanation

According to the passage, after implementing Ato's knowledge, the villagers successfully overcame their salt deficiency. They were able to grow healthy crops and were no longer weak and sickly, directly leading to improved health, food security, and overall prosperity for the community.

Explanation

According to the passage, Ato's village suffered from a generational salt deficiency that caused poor crops, weak health, and premature deaths. Ato traveled extensively to learn about salt and salt mining, then returned to teach the villagers how to cultivate crops requiring salt and build a salt mine. By successfully helping the villagers overcome their salt deficiency, he improved their overall health and living conditions, which is why he is remembered as the hero who saved his village.

Explanation

In the context of the passage, persistent describes Ato's unwavering determination and refusal to give up despite the initial skepticism of the villagers. Resolute means admirably purposeful, determined, and firm in one's course of action. Therefore, resolute serves as the exact synonym for persistent, accurately reflecting his steadfast effort to achieve his goal despite difficulties and resistance.

Explanation

In the given passage, "overcome" refers to successfully prevailing over or defeating the village's long-standing salt deficiency. The word "conquer" carries the exact same meaning of surmounting or defeating a major challenge or obstacle.

Explanation

The word "sceptical" describes someone who is doubtful, disbelieving, or hesitant to accept something as true, as seen in the passage where the villagers doubted that salt could help them. The word "trusting" means having complete faith, belief, or confidence in something without harboring doubt, making it the precise antonym of "sceptical".

Explanation

The proper logical order of the paragraph is C-B-D-E-A.

Sentence C introduces the main topic by defining the 17 Sustainable Development Goals (SDGs) and their broad global objective. Sentence B logically follows by identifying these goals as United Nations targets across specific sectors like health, education, and clean energy. Sentence D functions as the third sentence by elaborating on the specific pressing challenges the SDGs address, such as climate change and social injustice, while introducing the 2030 timeline. Sentence E expands on how collective global action achieves this vision, and sentence A provides the final concluding thought on the importance of embracing these goals for future generations.

Explanation

Sentence C introduces the main topic by defining the 17 Sustainable Development Goals (SDGs) as a comprehensive blueprint for global prosperity. Sentence B logically follows by elaborating on "these goals" established by the United Nations and outlining their interconnected targets. Sentence D expands on the specific pressing challenges the SDGs strive to address by 2030. Sentence E builds on this progress by describing how uniting nations and individuals in a collective effort allows the SDGs to envision a world balancing economic growth with social equity and environmental conservation. Finally, sentence A provides a natural conclusion on the importance of embracing these goals for future generations. The complete logical sequence is C-B-D-E-A, making sentence E the fourth sentence.

Explanation

The paragraph opens with sentence C, which introduces the concept of the 17 Sustainable Development Goals. Sentence B serves as the second sentence by using the demonstrative phrase "These goals" to expand upon the targets established by the United Nations. The full coherent sequence is C-B-D-E-A.

Explanation

To establish a logical flow, sentence C opens the paragraph by introducing the 17 Sustainable Development Goals (SDGs) as a global blueprint for prosperity. Sentence B follows sentence C by identifying the United Nations as the establishing body and detailing specific targets like health, education, and clean energy. Sentence D expands on sentence B by specifying the challenges the SDGs address, such as climate change and inequality, by 2030. Sentence E comes next, describing how collective effort among nations and individuals balances economic growth with environmental conservation and social equity. Finally, sentence A concludes the paragraph with a call to action on the necessity of embracing these goals for future generations. The complete sequence is C-B-D-E-A.

Explanation

Sentence C serves as the ideal introductory sentence because it introduces the central theme—the 17 Sustainable Development Goals (SDGs)—and defines their overarching purpose as a blueprint for global prosperity. The rest of the paragraph logically expands upon this foundation: sentence B references "these goals" and their United Nations origin, sentence D specifies the challenges they address, sentence E outlines the collective effort needed, and sentence A concludes with the importance of embracing them. Thus, sentence C provides the essential context required to begin the paragraph.

Explanation

Interchanging the words house and spool restores the logical and grammatical meaning of the sentence. A spool is a cylindrical object used for holding wound wire, making spool of wire the contextually appropriate phrase. Similarly, running a cable line from one end of the house to the other provides a meaningful physical location and distance for the action described.

Explanation

The sentence is grammatically sound and contextually meaningful as written. The singular subject "The GST Council" correctly takes the verb "needs" (A), followed by the infinitive structure "to meet" (B). The adverbial phrase "more often" (C) appropriately modifies how frequently they should meet, and "turn" (D) maintains parallel structure with "meet" following the infinitive marker "to" (needs to meet... and turn...). Since all words are in their syntactically correct positions, no interchange is required.

Explanation

In the original text, the action verb and location noun are inverted. Interchanging position B and position C places the verb after the subject noun and the location noun after the preposition, producing the grammatically sound sentence: "A grand procession rolled through the streets of the festive city."

Explanation

In the given sentence, the words "class" and "perk" are misplaced. A perk refers to an advantage or benefit, which fits contextually in the phrase "it was a perk to have his best friend...", while "class" correctly describes the academic environment where his friend is present ("in the same class"). Exchanging these two words restores the logical meaning and proper grammar of the sentence.

Explanation

The original sentence is grammatically sound and contextually coherent. Unravelling correctly describes the action of unwinding or untangling, fishing appropriately modifies line to form a standard noun phrase, wrapped logically depicts the state of the line around the spool, and prepared serves as the main past-tense verb indicating the action taken by the fisherman. Since each bold word fits its position in both syntax and meaning, no interchange is needed.

Explanation

The sequence CBAD forms a grammatically correct and logically coherent sentence describing the process of transpiration in plants. Part C introduces the temporal dependent clause with "once water is". Part B provides the passive verb and origin phrase "moved from the roots to". Part A completes the destination "the leaves", followed by a comma, and begins the main clause with "plants release the". Part D completes the sentence with the direct object and modifying phrase "excess liquid in the form of vapor." Together, they form the complete sentence: "Once water is moved from the roots to the leaves, plants release the excess liquid in the form of vapor."

Explanation

When a continuous past action is interrupted by a shorter, single event, English grammar rules require the past continuous tense for the ongoing action and the simple past tense after "when" for the interrupting action. In this sentence, "was going out" describes the ongoing action in the past, so the interrupting event taking place at that specific moment requires the simple past verb form "rang".

Explanation

In English grammar, the phrase "used to" expresses a past habit or repeated action and is always followed by the base form of the verb (bare infinitive). Therefore, the base verb "follow" correctly fits into the sentence to form "used to follow", indicating a routine action in the past.

Explanation

The verb 'evoked' means to elicit, call forth, or bring out a particular emotion, memory, or reaction in someone. In the context of artistic creation, an artist's unique style and vision naturally inspire or awaken feelings of wonder and awe among the viewers. Therefore, 'evoked' fits both contextually and grammatically to describe how the artwork produced a strong emotional response.

Explanation

To forge means to form, build, or create a strong bond, relationship, or connection through skill and effort. In this context, "forged" accurately describes how the musician's soulful performance and heartfelt lyrics successfully created and established a deep emotional connection with the audience.

Explanation

The word "ignited" metaphorically means to spark, trigger, or set off a sudden and intense reaction. In the given context, a sudden economic downturn acts as a catalyst that rapidly sparks widespread unpredictability and concern. It precisely describes how the unexpected economic drop triggered a swift wave of uncertainty among investors and business owners.

Explanation

Part C contains a grammatical error involving the incorrect use of the personal possessive pronoun. Animals, unless explicitly personified or identified by a specific gender, are referred to using the neuter possessive pronoun its rather than his or her. Since the small guppy is an animal without a specified gender in this context, his must be replaced with its, making the correct phrasing "its tailfin back and forth".

Explanation

The noun "police" is a plural collective noun that requires a plural verb form. In the phrase "police has not", the singular verb is grammatically incorrect and should be corrected to "police have not" to ensure proper subject-verb agreement.

Explanation

The prepositional phrase "associated for" is grammatically incorrect in this context. The adjective "associated" takes the preposition "with" when indicating a connection, relation, or link to something. Therefore, the phrase should correctly read "associated with the eyes".

Explanation

The preposition "about" requires an object, which must be either a noun phrase or a gerund phrase. The phrase "the market crashes" uses a finite present-tense verb form, which is grammatically incorrect following the preposition "about". It should be replaced with the gerund phrase "the market crashing" or the singular noun phrase "the market crash". The correct sentence is: "The investor sold all of his stocks after having a premonition about the market crashing".

Explanation

The sentence follows the standard Type 1 conditional structure (If + Present Simple, Future Simple) correctly: "If logical minds do not prevail..." sets the conditional clause in the present tense, while "...a major war will break out..." uses the future tense in the main clause. Additionally, the preposition "between" is used correctly when referring to two entities ("the two largest gangs"), and the plural subject "logical minds" correctly agrees with the plural auxiliary verb "do". Since all grammatical, idiomatic, and subject-verb agreement rules are fully satisfied, the sentence contains no errors.