Mathematics

When errors of 5% and 3% are made in the measurements of the sides of a rectangle, the percentage error in the calculated area is approximately the sum of the individual percentage errors plus their product. This is calculated as 5% + 3% + (5% × 3%) = 8.15%. Therefore, the correct answer is option C (8.15%).

The total votes are 1136 + 7636 + 11628 = 20400. The winning candidate received 11628 votes. The percentage is (11628 / 20400) × 100 ≈ 57%. However, since 57% is option A, the correct answer is A, not C. Recalculating: 11628/20400 = 0.57 or 57%. Therefore, the correct answer is A.

The man buys two articles for Rs.1980 each. On the first article, he gains 10%, so the selling price is 1980 + 10% of 1980 = Rs.2178. On the second article, he loses 10%, so the selling price is 1980 - 10% of 1980 = Rs.1782. The total cost price is 1980 + 1980 = Rs.3960. The total selling price is 2178 + 1782 = Rs.3960. Since the total selling price equals the total cost price, there is no overall gain or loss. Therefore, the total gain or loss percent is 0%, which corresponds to option D (no gain or no loss).

There are 1000 inhabitants, with 60% males (600 males) and 40% females (400 females). Among males, 20% are literate, so 600 * 0.20 = 120 literate males. Total literates are 25% of 1000 = 250. Therefore, literate females = 250 - 120 = 130. Percentage of literate females = (130 / 400) * 100 = 32.5%. However, the calculation shows 32.5%, but the correct answer given is C (32.5%). The options have a spacing error in option A and C, but the correct answer is C as per calculation.

To achieve a 25% profit on a cost price of Rs.47.50, the selling price must be Rs.47.50 × 1.25 = Rs.59.375. Since the article is sold after a 5% discount on the marked price, let the marked price be M. The selling price after discount is 95% of M, so 0.95 × M = 59.375. Solving for M gives M = 59.375 / 0.95 = Rs.62.50. Therefore, the article must be marked at Rs.62.50 to achieve the desired profit after the discount.

Let the original price be Rs. x per kg. After a 20% reduction, the price becomes 0.8x. With Rs. 120, the purchaser can buy 120/x kg originally and 120/(0.8x) kg after reduction. The difference is 3 kg: 120/(0.8x) - 120/x = 3. Solving gives x = Rs. 12.

Total votes = 7500; invalid votes = 20% of 7500 = 1500; valid votes = 7500 - 1500 = 6000. One candidate got 55% of valid votes = 0.55 × 6000 = 3300. The other candidate got the remaining valid votes = 6000 - 3300 = 2700. Therefore, the other candidate received 2700 valid votes, which corresponds to option A.

The population increased from 175,000 to 262,500 over 10 years. The total increase is 87,500, which is a 50% increase over 10 years. The average annual percent increase is calculated using the compound interest formula: (Final/Initial)^(1/10) - 1 = (262,500/175,000)^(0.1) - 1 ≈ 1.5^(0.1) - 1 ≈ 0.0437 or 4.37%.

Let the capacity of the bucket be x litres. The difference in volume between 80% and 66.5% fill is 2 litres. This gives the equation: 0.80x - 0.665x = 2, which simplifies to 0.135x = 2. Solving for x gives x = 2 / 0.135 ≈ 14.81 litres. Among the given options, 15 litres (option B) is the closest and correct answer. The original answer (D) 20 litres is incorrect based on this calculation.

When the length is increased by 10%, it becomes 1.1 times the original length. When the breadth is decreased by 10%, it becomes 0.9 times the original breadth. The new area is 1.1 × 0.9 = 0.99 times the original area, which means the area decreases by 1%.