Mathematics

If the price increases by 25%, the new price is 125% of the original. To keep expenditure the same, the quantity used must be reduced so that (new quantity) × (new price) = (original quantity) × (original price). This means new quantity = original quantity × (100/125) = 0.8 of original quantity, a 20% reduction.

The population increases at 5% per year. To find the population in 1978 (3 years before 1981), we calculate the population in 1981 divided by (1.05)^3, which gives approximately 120,000. Hence, option A is correct.

If the price is reduced by 25%, the new price is 75% of the original. To restore the original price, the new price must be increased by (25/75)*100 = 33 1/3%.

Let F_E be the percentage failing English = 38%, P_U be the percentage passing Urdu = 61%, so failing Urdu = 39%. Given 23% fail both subjects. Total failure percentage = fail English + fail Urdu - fail both = 38% + 39% - 23% = 54%. However, the question asks for actual failure percentage, which is the union of failures. Since 61% pass Urdu, 39% fail Urdu, and 38% fail English, with 23% failing both, total failure = 38% + 39% - 23% = 54%. But the options and question wording suggest actual failure percentage is the union of failures, which is 54%. The correct answer should be 54%, which corresponds to option C. Therefore, the original correct_answer 'C' is correct. The explanation was missing and has been added. Difficulty is medium due to percentage and set operations involved.

If the price is reduced by 25%, the new price is 75% of the original. To restore the original price, increase the new price by (25/75)*100 = 33 1/3%.

First, calculate the number of males: 65% of 6400 = 4160. Then, find the number of males at least 50 years old: 25% of 4160 = 1040. Finally, subtract to find males below 50 years: 4160 - 1040 = 3120.

The winner received 62% of the votes and won by 288 votes, meaning the difference between the winner's and loser's votes is 288. Let total votes be x. Then, 62% of x - 38% of x = 288, which simplifies to 24% of x = 288. So, x = 288 / 0.24 = 1200 total votes. The winning candidate's votes are 62% of 1200 = 744 votes. However, 744 is option B, so let's verify carefully: 62% - 38% = 24%, 24% of total votes = 288, total votes = 288 / 0.24 = 1200. Winning votes = 62% of 1200 = 744. Therefore, the correct answer is B, not C. The initial correct_answer was B, which is correct. The explanation was missing and has been added. The question text was corrected for grammar and clarity, and difficulty set to medium.

Subtracting 10% from X means taking away 10% of X, which is equivalent to multiplying X by 90% (or 0.9). This is because 100% - 10% = 90%.

Given A got 360 marks which is 10% less than B, B's marks = 360 / 0.9 = 400. B got 25% more than C, so C's marks = 400 / 1.25 = 320. C got 20% less than D, so D's marks = 320 / 0.8 = 400. The full marks are 500, so D's percentage = (400 / 500) * 100 = 80%. However, this calculation shows 80%, but the options show 80% as C and 90% as B. Rechecking: A = 360, A = 0.9 * B => B = 400; B = 1.25 * C => C = 320; C = 0.8 * D => D = 400. So D scored 400 marks, which is 80% of 500. Therefore, the correct answer is C (80%). The original correct_answer is C, which matches the calculation. The initial confusion was in the explanation. The correct answer is C (80%).

When the price of TV sets is decreased by 30%, the new price becomes 70% of the original price. The sales increase by 20%, so the quantity sold becomes 120% of the original quantity. The revenue is the product of price and quantity sold. Therefore, the new revenue is 70% × 120% = 84% of the original revenue, which means the revenue decreases by 16%. Hence, the revenue received by the shopkeeper decreases by 16%, corresponding to option D.