Mathematics

All four options (42624, 37573, 84284, 93339) are palindromic numbers, meaning they read the same forwards and backwards. Therefore, the odd one out cannot be identified based on palindromicity. However, option C (84284) is the only number composed entirely of even digits, while the others contain odd digits. This makes option C the odd one out based on digit parity.

A single discount of 40% on Rs. 500 is Rs. 200, so the price after discount is Rs. 300. Two successive discounts of 36% and 4% on Rs. 500 result in a net discount calculated as 36% + 4% - (36% × 4%) = 38.56%. The price after successive discounts is Rs. 500 × (1 - 0.3856) = Rs. 307.20. The difference between the two discounted prices is Rs. 307.20 - Rs. 300 = Rs. 7.20. Therefore, the difference between the discounts is Rs. 7.20, which corresponds to option D.

The successive discounts are applied one after another on the reducing price. Starting with Rs. 12,000, after 15% discount, price = 12000 × 0.85 = Rs. 10,200; after 10% discount, price = 10200 × 0.90 = Rs. 9,180; after 5% discount, price = 9180 × 0.95 = Rs. 8,721. Hence, the customer buys it at Rs. 8,721.

Successive discounts are not simply added. Instead, the combined discount is calculated by multiplying the remaining price fractions after each discount. A 20% discount leaves 80% of the price, and a 15% discount on the remaining 80% leaves 85% of 80%, which is 68% of the original price. Therefore, the single equivalent discount is 100% - 68% = 32%. This matches option C.

The total selling price for 85 meters of cloth is Rs. 8925, so the selling price per meter is Rs. 8925 ÷ 85 = Rs. 105. Since the trader makes a profit of Rs. 15 per meter, the cost price per meter is the selling price per meter minus the profit per meter, which is Rs. 105 - Rs. 15 = Rs. 90. Therefore, the cost price of one meter of cloth is Rs. 90, corresponding to option C.

To make a profit of 20% on an article bought at Rs.500, the selling price should be 500 + 20% of 500 = 500 + 100 = Rs.600. Hence, option A is correct.

Since the man sells the mixture at the same rate as milk but gains 20%, the cost price of the mixture is 20% less than the selling price. This means the mixture is 100% milk + water, where water is free. The ratio of water to milk is 1:5 to achieve a 20% gain.

The price after the first discount of 20% on Rs. 160 is Rs. 160 × 0.8 = Rs. 128. After the second discount of 10% on Rs. 128, the price is Rs. 128 × 0.9 = Rs. 115.20. Therefore, the amount the man pays is Rs. 115.20, which corresponds to option D.

If selling at Rs. 10.80 results in a 10% loss, the cost price (CP) is Rs. 12 (since 10.80 = 90% of CP). To earn 20% profit, the selling price should be 120% of CP, which is Rs. 14.40. However, the options given suggest a different calculation: 10.80 is 90% of CP, so CP = 10.80 / 0.9 = 12. To earn 20% profit, selling price = 12 × 1.20 = Rs. 14.40. Option C is Rs. 14.40, which matches this calculation. Therefore, the correct answer is C, not B. The original correct_answer was C, so it is correct. The explanation was missing and is now provided. The difficulty is easy, and tags are added accordingly.

If selling 12 toffees for 1 rupee causes a 20% loss, the cost price of 12 toffees is 1.25 rupees. To gain 20%, the selling price should be 1.2 times the cost price, so selling price for the same quantity is 1.5 rupees. Therefore, to sell at a gain of 20% for 1 rupee, the number of toffees should be 15.