SSC CGL Tier 1 2019 General Awareness Questions with Solutions

Explanation

In △ ABC, when the sides AB and AC are extended and the exterior bisectors of ∠ B and ∠ C meet at point O, the angle ∠ BOC is determined by the formula ∠ BOC = 90° - (∠ A)/(2). This relationship is a standard result in geometry concerning the ex-center of a triangle. Given that ∠ A = 92°, the calculation is as follows:

∠ BOC = 90° - (92°)/(2)

∠ BOC = 90° - 46°

∠ BOC = 44°

The formula is derived from the property that the sum of the angles in △ BOC is 180°, where the two base angles are half of the exterior angles at B and C, specifically ½(180° - ∠ B) and ½(180° - ∠ C). Summing these with ∠ BOC and substituting 180° - ∠ A for ∠ B + ∠ C yields the result.

Explanation

The production of type E cars in 2015 is 65 thousand and the production of type C cars in 2013 is 45 thousand. Combining these two figures gives a total of 65 + 45 = 110 thousand. Next, the total production of type A cars from 2012 to 2016 is the sum of its annual production: 46 + 48 + 56 + 57 + 64 = 271 thousand. Similarly, the total production of type D cars from 2012 to 2016 is 46 + 49 + 57 + 55 + 72 = 279 thousand. The collective production of type A and type D cars over the five-year period is 271 + 279 = 550 thousand. To determine the percentage, we apply the relation Percentage = (Specified Production / Total Production) × 100. This results in (110 / 550) × 100. Since 110 / 550 simplifies to 1 / 5, the final calculation yields 0.2 × 100, which is 20%.

Explanation

Based on the geometric property that tangents drawn from an external point to a circle are equal in length, we can determine the segments of the quadrilateral sides.

From point B, the tangents to the circle are BP and BQ. Given BP = 4 cm, it follows that BQ = 4 cm. Since the total length of side BC is given as 7 cm, the segment CQ is calculated as BC - BQ = 7 - 4 = 3 cm.

From point C, the tangents are CQ and CR. Therefore, CR = CQ = 3 cm. From point D, the tangents are DS and DR. Given SD = 6 cm, it follows that DR = 6 cm. To find the total length of side DC, we sum the segments DR and RC:

DC = DR + RC = 6 cm + 3 cm = 9 cm

Explanation

For a number to be divisible by 88, it must be divisible by both 8 and 11.

Divisibility by 8 requires the last three digits of the number, 8y2, to be divisible by 8. Testing values for the digit y: If y = 3, 832 ÷ 8 = 104 If y = 7, 872 ÷ 8 = 109 Thus, y can be 3 or 7.

Divisibility by 11 requires the difference between the sum of digits at odd places and the sum of digits at even places to be 0 or a multiple of 11. For the 10-digit number 1330x558y2: Sum of digits at odd positions (from the right): 2 + 8 + 5 + 0 + 3 = 18 Sum of digits at even positions (from the right): y + 5 + x + 3 + 1 = 9 + x + y Difference = 18 - (9 + x + y) = 9 - (x + y)

To satisfy the condition for 11, the value 9 - (x + y) must be a multiple of 11. Since x and y are single digits, the sum x + y can only range from 0 to 18. Setting the difference to 0: 9 - (x + y) = 0 ⟹ x + y = 9

Setting the difference to other multiples of 11, such as 11 or -11, would result in x + y = -2 or x + y = 20, both of which are impossible for single-digit sums. Therefore, the value of x + y is 9.

Explanation

The total efficiency of A, B, and C is 7 + 5 + 8 = 20 units per day. Given that they can complete the work in 42 days, the total work is calculated using the formula Total Work = Total Efficiency × Time, which gives 20 × 42 = 840 units. B and C work together for 21 days with a combined efficiency of 5 + 8 = 13 units per day, so they complete 13 × 21 = 273 units. The remaining work is 840 - 273 = 567 units. A completes this remaining work alone with an efficiency of 7 units per day, taking 567 / 7 = 81 days. The whole work was completed in the time spent by B and C plus the time spent by A alone, which is 21 + 81 = 102 days.

Explanation

On March 23, 1931, the British colonial government executed revolutionary freedom fighters Bhagat Singh, Sukhdev Thapar, and Shivaram Rajguru by hanging them in the Lahore Central Jail. They were convicted for the assassination of British police officer John Saunders in 1928, an act carried out to avenge the death of Lala Lajpat Rai. To commemorate their bravery and ultimate sacrifice in the struggle for India's independence, March 23 is officially observed across the country as Shaheed Diwas, or Martyrs' Day. This day serves as a national tribute to their revolutionary spirit and their significant contributions to the Indian freedom movement.

Explanation

The Ganga is the longest river in India, flowing for approximately 2,525 km within the country's borders. Although the Brahmaputra and Indus have longer total lengths, the majority of their flow occurs outside of India.

Explanation

Prince Salim, the eldest son of the Mughal Emperor Akbar, ascended the throne in 1605. Upon his accession, he adopted the imperial title Nur-ud-din Muhammad Jahangir. This title is derived from the Persian words Jahan, meaning world, and gir, meaning seizer or conqueror, effectively translating to Conqueror of the World. He was the fourth ruler of the Mughal dynasty and is remembered for his administrative stability and patronage of the arts, particularly Mughal painting. His reign lasted until 1627, during which he maintained the vast empire inherited from his father.

Explanation

Indira Gandhi served as the Prime Minister of India from 1966 to 1977 and was the head of government during the internal Emergency. On her recommendation, President Fakhruddin Ali Ahmed invoked Article 352 of the Indian Constitution to declare a state of National Emergency on June 25, 1975. This period lasted for 21 months until its revocation on March 21, 1977. During this time, the Prime Minister exercised extraordinary powers, leading to the suspension of fundamental rights and the postponement of general elections. The Emergency remains one of the most significant periods in India's post-independence political history, ending only after the 1977 general elections were called.

Explanation

The Victoria Memorial is a monumental marble building located in Kolkata, which served as the capital of British India during the early 20th century. Following the death of Queen Victoria in 1901, Lord Curzon, the then Viceroy of India, proposed the creation of a majestic memorial that would serve both as a tribute to the deceased Empress and as a historical museum. Designed by the architect William Emerson in the Indo-Saracenic revival style, the structure incorporates Mughal and European architectural elements. Built using Makrana marble, the memorial is widely regarded as the architectural climax of Kolkata, symbolizing the city's status as the premier center of British imperial power in India before the capital was shifted to Delhi in 1911.

Explanation

World Meteorological Day is celebrated annually on 23 March to commemorate the formal establishment of the World Meteorological Organization (WMO) in 1950. The organization functions as the specialized agency of the United Nations for meteorology, operational hydrology, and related geophysical sciences. The theme for 2019, The Sun, the Earth and the weather, was chosen to highlight the fundamental influence of the Sun on the Earth atmosphere, oceans, and weather cycles. By focusing on this theme, the WMO aimed to showcase the essential work of National Meteorological and Hydrological Services in monitoring the Sun energy and its impact on the planet's changing climate and daily weather conditions.

Explanation

Commander Abhilash Tomy was the sole Asian participant in the 2018 Golden Globe Race, an elite solo circumnavigation event that required sailors to use technology available only in 1968. He sailed on the Thuriya, a replica of the Suhaili used by Sir Robin Knox-Johnston in the original race. A veteran sailor of the Indian Navy, Tomy had already completed a solo non-stop circumnavigation in 2013 as part of the Sagar Parikrama II mission. His entry into the 2018 race was significant as it marked the 50th anniversary of the first-ever solo non-stop voyage around the world.

Explanation

The 1903 Nobel Prize in Physics was awarded jointly to Henri Becquerel, Pierre Curie, and Marie Curie for their pioneering work on radiation phenomena. Henri Becquerel was recognized for his discovery of spontaneous radioactivity, while the Curies were honored for their extensive research into the radiations discovered by Becquerel. Marie Curie coined the term radioactivity to describe the spontaneous emission of particles or energy from the atomic nucleus. Their collective research proved that atoms were not indivisible or stable, laying the essential groundwork for modern nuclear physics and the study of subatomic particles.

Explanation

Fiscal deficit is the difference between the total expenditure of the government and its total receipts, excluding borrowings. It serves as an indicator of the total borrowing requirements of the government from all sources during a financial year. The mathematical representation is:

Fiscal Deficit = Total Expenditure - (Revenue Receipts + Non-debt Capital Receipts)

In this context, non-debt capital receipts include items such as the recovery of loans and proceeds from the disinvestment of public sector undertakings. Because the calculation specifically excludes money obtained through borrowings, the resulting figure represents the budgetary gap that must be financed through debt, whether from the central bank, domestic financial markets, or external sources. It is a key macroeconomic indicator used to assess the financial health and fiscal discipline of a country.

Explanation

Santiago Ramon y Cajal was awarded the Nobel Prize in Physiology or Medicine in 1906, sharing the honor with Camillo Golgi for their work on the structure of the nervous system. Cajal is celebrated as the father of modern neuroscience for establishing the neuron doctrine. Using the Golgi staining method, he provided histological evidence that the nervous system is composed of individual, discrete cells called neurons, rather than a continuous interconnected web. His research demonstrated that neurons communicate with each other across specialized gaps, a discovery that fundamentally changed the scientific understanding of how the brain and nervous system function.

Explanation

Throughout the British colonial period, India's foreign trade was characterized by a consistent and substantial export surplus. This meant that the value of exports, which primarily consisted of raw materials such as cotton, silk, indigo, wool, and food grains, regularly exceeded the value of imports, which were mostly finished manufactured products from Britain. However, this export surplus did not result in an inflow of gold or silver to benefit the Indian economy. Instead, the surplus was utilized to finance the Drain of Wealth from India to Britain. It was used to pay for Home Charges, which included the salaries and pensions of British civil and military officials, interest on debts incurred by the colonial government, and expenses for wars fought by the British Empire. This mechanism ensured that the economic gains from India's trade were siphoned off to sustain British administrative and imperial interests.

Explanation

William Crookes discovered the element thallium in 1861 through the use of flame spectroscopy. While examining the spectroscopic signature of selenium residues from a sulfuric acid factory, he observed a previously unknown bright green line. He named the element thallium after the Greek word thallos, which signifies a green shoot or budding twig, reflecting the distinct color of its spectral emission. His research was further solidified when he succeeded in isolating the element in its metallic form the following year.

Explanation

Justice Adarsh Kumar Goel was appointed as the Chairperson of the National Green Tribunal (NGT) on July 6, 2018, which coincided with his retirement as a judge of the Supreme Court of India. The Appointments Committee of the Cabinet approved his appointment for a term of five years. The position of the NGT Chairperson had been vacant since December 2017 following the retirement of Justice Swatanter Kumar. During his tenure at the Supreme Court, Justice Goel was involved in several significant rulings, and his appointment to the NGT was intended to address the backlog of environmental cases and provide judicial leadership to the specialized environmental body.

Explanation

Maharaja Sawai Pratap Singh, the grandson of Maharaja Sawai Jai Singh II, commissioned the construction of the Hawa Mahal in Jaipur in 1799. Designed by the architect Lal Chand Ustad, this five-story structure is built from red and pink sandstone and is unique for its 953 small windows known as jharokhas. These windows were intricately designed with latticework to allow the royal ladies to observe daily life and festivals in the streets below while maintaining the strict custom of purdah, as they remained invisible from the outside. The architectural design also facilitates the Venturi effect, ensuring a constant flow of cool air throughout the palace.

Explanation

Mughal Emperor Shah Jahan commissioned the construction of the Red Fort and the Jama Masjid in Delhi during the mid-17th century when he shifted his capital from Agra to Shahjahanabad. Shah Jahan's reign is considered the golden age of Mughal architecture.

Explanation

Mohammed Hussamuddin clinched the silver medal in the 56kg bantamweight category at the 38th GeeBee Boxing Tournament held in Helsinki, Finland, in March 2019. He reached the final after a strong performance in the earlier rounds, including a victory over Kazakhstan's Zhanbolat Kydyrbayev in the semifinals. In the gold medal bout, he faced fellow Indian boxer Kavinder Singh Bisht and finished with the silver medal after a closely contested match. This tournament was a significant event for the Indian boxing contingent, which secured a total of eight medals during the competition.

Explanation

The Yangtze River, also known as the Chang Jiang, is the longest river in Asia and the third-longest in the world. It flows for approximately 6,300 kilometers entirely within China, originating in the glaciers of the Qinghai-Tibet Plateau and travelling eastward before emptying into the East China Sea near Shanghai. The river basin drains one-fifth of the land area of the People's Republic of China and is home to nearly one-third of the country's population. It serves as a vital artery for transportation, agriculture, and hydroelectric power, including the operation of the Three Gorges Dam, which is the world's largest power station by installed capacity.

Explanation

J.J. Thomson discovered the electron in 1897 through his experiments with cathode ray tubes. He demonstrated that cathode rays were composed of previously unknown negatively charged particles, which he calculated to have a much smaller mass than the lightest known atom. By measuring the ratio of the electrical charge to the mass of the particle, denoted as e/m, Thomson proved that these corpuscles were universal constituents of all matter. This discovery revolutionized the understanding of atomic structure, proving that atoms were not indivisible but contained subatomic particles.

Explanation

Jalal-ud-din Muhammad Akbar was born in 1542 at the fortress of Umarkot in Sindh while his father, Humayun, was living in exile following his defeat by Sher Shah Suri. When Humayun passed away in 1556 after a fall from his library stairs in Delhi, Akbar was just 13 years old. He was crowned at Kalanaur in Punjab under the regency of Bairam Khan, who managed the affairs of the Mughal Empire until Akbar reached maturity.

Explanation

Shah Jahan, the fifth Mughal Emperor, commissioned the construction of the Taj Mahal in 1632 as a grand mausoleum for his beloved wife, Arjumand Banu Begum, who was known by the title Mumtaz Mahal. Situated on the southern bank of the Yamuna River in Agra, the monument is considered the finest example of Mughal architecture, incorporating Persian, Islamic, and Indian design elements. The construction of the main mausoleum was completed in 1643, though work on the entire complex continued for another decade. Built using white marble and decorated with intricate pietra dura inlay work of semi-precious stones, the structure serves as the final resting place for both Mumtaz Mahal and Shah Jahan himself.

Explanation

The Danube is recognized as the river that passes through the greatest number of countries in the world. Originating in the Black Forest region of Germany, it flows in a southeasterly direction for approximately 2,850 kilometers before reaching the Black Sea. Along its course, the river flows through or forms the borders of ten different nations: Germany, Austria, Slovakia, Hungary, Croatia, Serbia, Romania, Bulgaria, Moldova, and Ukraine. Its drainage basin also encompasses parts of several other countries, making it one of the most significant international maritime routes and a crucial ecological corridor for the European continent.

Explanation

In its March 2019 Global Economic Outlook report, Fitch Ratings lowered India's GDP growth forecast for the fiscal year 2019-20 to 6.8% from its previous estimate of 7%. This downward revision was driven by a slower-than-expected recovery in the manufacturing sector and agriculture, alongside a deceleration in credit growth. The agency noted that while monetary policy easing was expected to support growth, the momentum had weakened compared to earlier projections.

Explanation

The 86ᵗʰ Constitutional Amendment Act, 2002, inserted Article 21A into the Constitution of India, which declares that the State shall provide free and compulsory education to all children of the age of six to fourteen years as a Fundamental Right. This amendment also substituted Article 45 in the Directive Principles of State Policy, directing the State to provide early childhood care and education for all children until they complete the age of six years. Additionally, it added a new Fundamental Duty under Article 51A(k), making it the responsibility of a parent or guardian to provide opportunities for education to their child or ward between the age of six and fourteen years.

Explanation

Wilhelm Conrad Röntgen was a German physicist who produced and detected electromagnetic radiation in a wavelength range known as X-rays or Röntgen rays on November 8, 1895. This discovery occurred while he was investigating the external effects from various types of vacuum tube equipment when an electrical discharge was passed through them. He observed that these rays could pass through human tissue, allowing for the visualization of internal structures like bones. In 1901, the Nobel Committee awarded him the inaugural Nobel Prize in Physics in recognition of the extraordinary services he rendered by the discovery of the remarkable rays subsequently named after him.

Explanation

Dinesh Dagar secured a silver medal in the 69kg welterweight category at the 38th GeeBee Boxing Tournament held in March 2019 in Helsinki, Finland. He advanced to the final after a significant victory over former Olympic medalist Evaldas Petrauskas but eventually lost the gold medal bout to England’s Pat McCormack. Consequently, he was a silver medalist rather than one of the three Indian bronze medalists at the event.

Explanation

The principal amount x borrowed and paid back in equal installments is calculated as the sum of the present values of each installment. For two equal yearly installments I at an annual interest rate r, the formula is: x = (I)/(1 + r){100} + (I)/((1 + r){100)²}

Given the installment I = 35280 and the rate r = 5%, the factor 1 + ʳ⁄₁₀₀ is 1 + ⁵⁄₁₀₀ = ²¹⁄₂₀. Substituting these values into the formula: x = (35280)/(21/20) + (35280)/((21/20)²) x = 35280 × ²⁰⁄₂₁ + 35280 × ⁴⁰⁰⁄₄₄₁

To simplify the calculation, factor out common terms: x = ³⁵²⁸⁰⁄₄₄₁ × (20 × 21 + 400) x = 80 × (420 + 400) x = 80 × 820 x = 65600

Explanation

In the right-angled triangle ABC, where ∠A = 90°, we apply the Pythagorean theorem to find the length of side AB. The relationship is AB² + AC² = BC². Substituting the given values AC = 6 cm and BC = 10 cm, we get AB² + 6² = 10², which simplifies to AB² + 36 = 100. Solving for AB, we find AB² = 64, so AB = 8 cm.

Point D lies on segment AB such that BD = 4 cm. Therefore, the length of AD is AB - BD = 8 - 4 = 4 cm. Now, considering the right-angled triangle CAD (where ∠A remains 90°), we apply the Pythagorean theorem again to find CD. The relationship is CD² = AC² + AD². Substituting the values AC = 6 cm and AD = 4 cm, we get CD² = 6² + 4² = 36 + 16 = 52. Thus, CD = √(52) = √(4 × 13) = 2√(13) cm.

Explanation

Since points A, B, C, and D lie on a circle, ABCD is a cyclic quadrilateral. In a cyclic quadrilateral, the sum of opposite angles is 180°. Given ∠ADC = 130°, the opposite angle ∠ABC = 180° - 130° = 50°.

As AB is the diameter of the circle, the angle subtended by the diameter at the circumference is always a right angle. Therefore, ∠ACB = 90°.

In △ABC, the sum of all interior angles is 180°. Applying this property, we have ∠BAC + ∠ABC + ∠ACB = 180°. Substituting the calculated values, ∠BAC + 50° + 90° = 180°. Solving for ∠BAC gives ∠BAC = 180° - 140° = 40°.

Explanation

The given equation 9a² + 4b² + c² + 21 = 12a + 4b - 8c can be rearranged by grouping terms of the same variable to form perfect squares.

Rearranging the terms: 9a² - 12a + 4b² - 4b + c² + 8c + 21 = 0

We can split the constant 21 into 4 + 1 + 16 to complete the squares for each variable: ((3a)² - 2(3a)(2) + 2²) + ((2b)² - 2(2b)(1) + 1²) + (c² + 2(c)(4) + 4²) = 0 (3a - 2)² + (2b - 1)² + (c + 4)² = 0

For the sum of squares of real numbers to be zero, each individual term must be zero: 3a - 2 = 0 ⟹ a = ⅔ 2b - 1 = 0 ⟹ b = ½ c + 4 = 0 ⟹ c = -4

Substituting these values into the required expression (9a + 4b - c): 9(⅔) + 4(½) - (-4) = 6 + 2 + 4 = 12

Explanation

To find the required ratio, first calculate the sum of the production for the specified categories using the values provided in the table. The production of type B cars in 2011 is 56 units and type E cars in 2013 is 64 units. The combined total for this group is 56 + 64 = 120.

Next, determine the production of type C cars in 2014, which is 56 units, and type D cars in 2012, which is 44 units. The combined total for this second group is 56 + 44 = 100. The ratio of the first group to the second group is expressed as 120 : 100. Dividing both sides by the greatest common divisor, which is 20, yields the simplified ratio of 6 : 5.

Explanation

To find the relationship between B and C, express each variable in terms of the others using the given percentages: A = B - 0.20B = 0.8B C = D + 0.20D = 1.2D D = A - 0.25A = 0.75A

Substitute the expression for A into the equation for D: D = 0.75 × (0.8B) = 0.6B

Now, substitute this expression for D into the equation for C: C = 1.2 × (0.6B) C = 0.72B

Explanation

The relationship between total selling price, quantity, and gain or loss percentage is given by the formula SP₁{Q₁ × (100 ± r₁)} = SP₂{Q₂ × (100 ± r₂)}. Here, SP represents the total selling price, Q represents the number of articles, and r represents the percentage of profit or loss.

Substituting the given values for the first case, where 25 articles are sold for ₹2,500 at a 10% loss, we get (2500)/(25 × (100 - 10)) = (2500)/(25 × 90) = ¹⁰⁰⁄₉₀. For the second case, we need to find the number of articles Q₂ to be sold for ₹2,400 to achieve a 20% profit. This gives the expression (2400)/(Q₂₎×₍₁₀₀₊₂₀₎ = (2400)/(Q₂₎×₁₂₀ = (20)/(Q₂₎. By equating the two ratios, ¹⁰⁰⁄₉₀ = (20)/(Q₂₎, and solving for Q₂, we find Q₂ = (20 × 90)/(100) = 18.

Explanation

The expression is in the form a³ - b³{a - b} = a² + b² + ab. By comparing the terms, we let a = 3√5x and b = √2y. Since (3√5x)³ = 27 × 5√5x³ = 135√5x³ and (√2y)³ = 2√2y³, the division yields: a² + b² + ab = (3√5x)² + (√2y)² + (3√5x)(√2y) a² + b² + ab = 45x² + 2y² + 3√(10)xy

Comparing this result with the given expression Ax² + By² + √(10)Cxy, we find the coefficients: A = 45 B = 2 C = 3

The value of A + B - 9C is calculated as: 45 + 2 - 9(3) = 47 - 27 = 20

Explanation

In the circle with center O and radius R = 10 cm, consider the triangle POQ. The lengths of the sides are OP = 10 cm, OQ = 10 cm, and PQ = 12 cm. To find the area of △POQ, we can drop a perpendicular from O to the chord PQ. Since OP = OQ, this perpendicular bisects PQ at a point K, making PK = KQ = 6 cm. In the right-angled triangle OKQ, the height OK = √(OQ² - KQ²) = √(10² - 6²) = 8 cm. The area of △POQ is ½ × PQ × OK = ½ × 12 × 8 = 48 cm².

Because PQ = PR, the points Q and R are symmetric with respect to the line passing through the center O and the point P. Thus, OP is the perpendicular bisector of the chord QR. Let M be the point of intersection of OP and QR. In △POQ, QM is the altitude drawn to the side OP. The area of △POQ can also be expressed as ½ × OP × QM. Substituting the known values, we get 48 = ½ × 10 × QM, which gives QM = 9.6 cm. Since M is the midpoint of QR, the total length of the chord QR = 2 × QM = 2 × 9.6 = 19.2 cm.

Explanation

For a number to be divisible by 72, it must be divisible by 8 and 9. For divisibility by 8, the last three digits 7x2 must be divisible by 8, which gives possible values for x as 1, 5, or 9. For divisibility by 9, the sum of the digits (50 + x + y) must be divisible by 9, meaning x + y must be 4 or 13. Testing the pairs, we get (x=1, y=3), (x=5, y=8), and (x=9, y=4). The greatest possible value of y is 8 (when x=5), so the value of 3x - y is 3(5) - 8 = 7.

Explanation

For the triangular field with sides a = 50 m, b = 70 m, and c = 80 m, the semi-perimeter s is calculated using the formula s = (a + b + c)/(2). Substituting the values, s = (50 + 70 + 80)/(2) = 100 m. The area A is then found using Heron's formula A = √(s(s-a)(s-b)(s-c)). This gives A = √(100(100-50)(100-70)(100-80)) = √(100 × 50 × 30 × 20) = √(3,000,000) = 1000√3 square metres.

The area of an equilateral triangle with side x is given by the formula √3{4}x². Equating the two areas, we get √3{4}x² = 1000√3. By canceling √3 from both sides, the equation simplifies to x² = 4000. Therefore, x = √(4000) = 20√(10). Using the approximation √(10) ≈ 3.162, we calculate x ≈ 20 × 3.162 = 63.24 m, which is closest to the value 63.2.

Explanation

The average production of all car types in 2014 is determined by summing the production values for types A, B, C, D, and E in that year, which is 63 + 64 + 56 + 65 + 72 = 320. The average is 320/5 = 64. The combined production of type B cars in 2013 and type D cars in 2010 is 68 + 42 = 110. To find the percentage by which the average is less than this combined total, use the formula (Total - Average)/(Total) × 100. Substituting the values gives (110 - 64)/(110) × 100 = 46/110 × 100 = 460/11 ≈ 41.81%. This rounds to approximately 41.8%.

Explanation

Let the total work be 1 unit. A can finish the work alone in 48 days, so the rate of work of A is r_A = ¹⁄₄₈ units per day. Since B begins the work and they work on alternate days, the work schedule for 11 ⅓ days is distributed as follows: B works on the odd-numbered days (1, 3, 5, 7, 9, 11), totaling 6 full days. A works on the even-numbered days (2, 4, 6, 8, 10) and the remaining fractional part of the 12th day, totaling 5 + ⅓ = ¹⁶⁄₃ days.

The amount of work completed by A is the product of A's rate and time: ¹⁶⁄₃ × ¹⁄₄₈ = ¹⁶⁄₁₄₄ = ⅑ units. The remaining work completed by B is 1 - ⅑ = ⁸⁄₉ units. Since B performed this work over 6 days, B's rate of work is r_B = (8/9)/(6) = ⁸⁄₅₄ = ⁴⁄₂₇ units per day.

To find the time B alone takes to finish 4 times the same work, we divide the new total work by B's rate: Time = (4 × 1)/(4/27) = 4 × ²⁷⁄₄ = 27 days.

Explanation

The selling price SP is given as 492 after an 18% discount on the marked price MP. We calculate the marked price using the formula MP = (SP)/(1 - Discount Rate). Substituting the values:

MP = (492)/(1 - 0.18) = (492)/(0.82) = ⁴⁹²⁰⁰⁄₈₂ = 600

If no discount is allowed, the selling price equals the marked price (600). In this scenario, the shopkeeper earns a 20% profit on the cost price CP. The relationship between the selling price and cost price is SP = CP × (1 + Profit Rate). Using 600 as the selling price:

600 = CP × (1 + 0.20) 600 = CP × 1.2 CP = (600)/(1.2) = ⁶⁰⁰⁰⁄₁₂ = 500

Explanation

Let the initial prices of articles A and B be 400 and 500. The price of B is decreased by 30%, making the new price 500 × 0.7 = 350. The new ratio of prices of A and B is given as 10 : 7. Since the 7 units in this ratio correspond to the actual value of 350, one unit equals 50.

The new price of A corresponds to 10 units in the ratio, so its value is 10 × 50 = 500. The price of article A increased from 400 to 500, representing an absolute increase of 100. The percentage increase x is calculated as: x = (500 - 400)/(400) × 100 = ¹⁰⁰⁄₄₀₀ × 100 = 25

Explanation

The Almatti Dam, also known as the Lal Bahadur Shastri Dam, is a major hydroelectric project constructed on the Krishna River in the Bagalkot district of North Karnataka. The dispute between Karnataka and Andhra Pradesh centered primarily on the height of the dam and the subsequent storage of water. Karnataka proposed to raise the height of the dam to 524.256 meters to increase its irrigation capacity and power generation. Andhra Pradesh, being the lower riparian state, raised objections on the grounds that increasing the dam height would significantly reduce the flow of water into its territory, thereby starving its own irrigation projects and the Krishna delta region of essential water resources. This inter-state water sharing conflict was a significant legal battle adjudicated by the Krishna Water Disputes Tribunal and the Supreme Court of India.

Explanation

Katrina Kaif was officially named the ambassador for Educate Girls in March 2018 to advocate for the education of girls in rural and underserved areas of India. Educate Girls is a non-profit organization that partners with the government and local communities to identify out-of-school girls and ensure their enrollment and retention in the formal education system. Through this partnership, she aimed to leverage her platform to highlight the systemic barriers preventing girls from accessing schools and to promote gender equality in education across the country.

Explanation

Under Article 331 of the Indian Constitution, the President was empowered to nominate two members of the Anglo-Indian community to the Lok Sabha if he believed the community was not adequately represented in the House. This provision was designed to ensure that the interests of this specific minority group were voiced in the legislature. As of July 2019, this constitutional rule established the maximum number of nominated members as two. This practice continued until it was eventually discontinued by the 104th Constitutional Amendment Act, which came into effect later in January 2020.

Explanation

Hiuen Tsang, the renowned Chinese Buddhist monk and scholar, visited India during the 7th century CE, specifically between 629 and 645 CE. His journey took place during the reign of King Harshavardhana, the ruler of the Pushyabhuti dynasty who governed much of North India from his capital at Kanauj. Hiuen Tsang's primary objective was to collect authentic Buddhist scriptures and visit sites associated with the life of the Buddha. He spent several years studying at the Nalanda University and became a close associate of Harsha, who invited him to preside over a major religious assembly at Kanauj. His detailed travel account, Si-Yu-Ki (Records of the Western World), remains a vital primary source for the history of Harsha's administration and the contemporary socio-economic state of India.

Explanation

The Index of Industrial Production (IIP) is a key economic indicator used to measure the growth of various industrial sectors in India, including mining, manufacturing, and electricity. In May 2017, the Central Statistical Office (CSO), under the Ministry of Statistics and Programme Implementation (MoSPI), revised the base year for the IIP from 2004-05 to 2011-12. This revision was implemented to better reflect the evolving structure of the Indian industry, incorporate new products, and align the index with other macroeconomic data series such as the Gross Domestic Product (GDP) and the Wholesale Price Index (WPI), which also use 2011-12 as their base year.