Mathematics

Ramees sells 900 grams of goods but charges for 1 kilogram (1000 grams) at cost price. The gain arises because he gives less quantity but charges for the full kilogram. The gain percent is calculated as ((1000 - 900) / 900) × 100 = (100 / 900) × 100 = 11 1/9%. This matches option C, not B as originally stated.

The loss is Rs.600 - Rs.500 = Rs.100. Loss percent = (Loss / Cost Price) × 100 = (100 / 600) × 100 = 16 2/3%.

When the side of a square is increased by 25%, the new side length is 1.25 times the original. The area increases by (1.25)^2 - 1 = 1.5625 - 1 = 0.5625, or 56.25%.

Let the original price per dozen bananas be Rs x. After a 40% reduction, the price becomes 0.6x. With Rs 40, the man can buy 40/x dozens originally, and after reduction, 40/(0.6x) dozens. The difference in quantity is 64 bananas, which is 64/12 = 16/3 dozens. So, 40/(0.6x) - 40/x = 16/3. Solving this gives x = Rs 5, so the reduced price is 0.6 * 5 = Rs 3 per dozen.

Given that X is 20% less than Z, X = 0.8Z. Given that Y is 28% less than Z, Y = 0.72Z. To find by what percentage Y is less than X, calculate ((X - Y) / X) × 100 = ((0.8Z - 0.72Z) / 0.8Z) × 100 = (0.08Z / 0.8Z) × 100 = 10%. Therefore, Y is 10% less than X. The correct answer is option C (10%).

Let the two numbers be 5x and 4x. Their difference is 5x - 4x = x = 10, so x = 10. The largest number is 5x = 50, which corresponds to option B.

Let the original price of one eraser be x rupees. For 1 rupee, the person can buy 1/x erasers. After a 25% price reduction, the new price is 0.75x, so the number of erasers for 1 rupee is 1/(0.75x) = 4/(3x). Given that the person can buy 2 more erasers for 1 rupee after the discount, we have 4/(3x) = 1/x + 2. Solving this gives x = 0.25, so originally 4 erasers could be bought for 1 rupee.

The single equivalent discount for a series of discounts is calculated by multiplying the complements of each discount and subtracting from 1. Here, (1-0.20)*(1-0.10)*(1-0.05) = 0.80*0.90*0.95 = 0.684, so the equivalent single discount is 1 - 0.684 = 0.316 or 31.6%.

Let the original price per kg be x. With a 20% reduction, the new price is 0.8x. For Rs.100, the lady can buy 100/x kgs originally and 100/(0.8x) kgs after the reduction. The difference is 10 kgs, so 100/(0.8x) - 100/x = 10. Solving gives x = 2 2/3.

The dealer claims to sell 1 kg but actually gives only 900 gm. The gain is on the difference of 100 gm over 900 gm, so gain percent = (100/900)*100 = 11 1/9%.