Mathematics

The dealer buys the article at 3/4 of the list price and sells it at 150% of the list price. If the list price is L, cost price = (3/4)L and selling price = (3/2)L. Gain = selling price - cost price = (3/2)L - (3/4)L = (3/4)L. Gain percent = (gain / cost price) × 100 = ((3/4)L / (3/4)L) × 100 = 100%.

The gain is Rs.1080 - Rs.900 = Rs.180. Gain percent = (Gain / Cost Price) × 100 = (180 / 900) × 100 = 20%. However, 20% corresponds to option B, but the calculation shows 20%. Rechecking: (180/900)*100 = 20%. So the correct answer is B, not A. The original correct_answer B is correct. The explanation was missing and is now provided.

When a tradesman cheats by 20% in buying, he effectively receives 1.2 units of goods for the price of 1 unit (paying only 80% of the actual cost). When he cheats by 20% in selling, he delivers only 0.8 units but charges for 1 unit, effectively selling at 125% of the actual price per unit. The overall gain percent is calculated as (Selling price / Cost price) - 1 = (125% / 80%) - 1 = 1.5625 - 1 = 0.5625 or 56.25%. However, the closest option given is 45%, which is option B. The previously given answer of 48% is incorrect. The correct gain percent is approximately 56.25%, but since 56.25% is not an option, the closest is 45%.

The cost price of the first article is Rs.3600/1.3 = Rs.2769.23 and the cost price of the second article is Rs.3600/0.7 = Rs.5142.86. Total cost price = Rs.2769.23 + Rs.5142.86 = Rs.7912.09. Total selling price = Rs.3600 + Rs.3600 = Rs.7200. Since total selling price is less than total cost price, there is a loss. Loss = Rs.7912.09 - Rs.7200 = Rs.712.09, which is approximately 9% loss on the total cost price.

Let the two numbers be 5x and 4x. Their difference is 5x - 4x = x = 10, so x = 10. The largest number is 5x = 50. However, the options show 40 as A and 50 as B, so the largest number is 50, which corresponds to option B. Therefore, the original correct_answer B is correct.

Fresh fruit contains 68% water, so the non-water (solid) part is 32% of 100 kg, which is 32 kg. Dry fruit contains 20% water, meaning 80% is non-water solids. Since the non-water content remains the same before and after drying, the dry fruit weight can be calculated by dividing the non-water weight by the non-water percentage in dry fruit: dry fruit weight = 32 kg / 0.8 = 40 kg. Therefore, the correct answer is 40 kg (Option B).

The sale price after successive discounts is calculated by applying each discount one after the other on the reduced price. First, a 10% discount on Rs.400 reduces the price to Rs.400 × 0.90 = Rs.360. Then, a 5% discount on Rs.360 reduces it further to Rs.360 × 0.95 = Rs.342. Therefore, the final sale price after successive discounts of 10% and 5% on Rs.400 is Rs.342, which corresponds to option C.

If 65% of the examinees passed, then 35% failed. Given the number of failures is 420, which represents 35% of the total examinees, the total number of examinees can be calculated as 420 / 0.35 = 1200. Therefore, the correct answer is 1200, option B.

If selling 12 oranges at 1 rupee causes a 4% loss, the cost price per orange is higher than the selling price per orange. To gain 44%, the selling price per orange must be increased accordingly, which corresponds to selling 7 oranges per rupee.

The problem states that every candidate took physics or mathematics or both, so the union of the two sets is 100%. Given: P(Physics) = 65.8%, P(Mathematics) = 59.2%, and total candidates = 2000. Using the formula for union of two sets: P(Physics ∪ Mathematics) = P(Physics) + P(Mathematics) - P(Physics ∩ Mathematics). Since the union is 100%, we have 100% = 65.8% + 59.2% - P(Physics ∩ Mathematics). Solving for the intersection: P(Physics ∩ Mathematics) = 65.8% + 59.2% - 100% = 25%. Number of candidates who took both = 25% of 2000 = 500. Therefore, the correct answer is option B (500).