Mathematics

The shopkeeper buys 4 mangoes for 1 rupee, so the cost price per mango is 1/4 rupee. He sells 3 mangoes for 1 rupee, so the selling price per mango is 1/3 rupee. The cost price for 3 mangoes is 3 × (1/4) = 3/4 rupee, and the selling price for 3 mangoes is 1 rupee. Profit = 1 - 3/4 = 1/4 rupee. Profit percent = (Profit / Cost Price) × 100 = (1/4) / (3/4) × 100 = 33 1/3%.

The problem involves calculating the marked price based on the difference in profit when the discount changes from 5% to 7%. By setting up equations for profit at both discount rates and using the Rs. 15 difference, the marked price is found to be Rs. 712.50.

Let the marked price be M. The retailer gets a 15% discount, so he buys the machine at 85% of M, i.e., 0.85M. He sells it for Rs. 1955 and makes a 15% profit on his cost price (0.85M). Therefore, selling price = cost price × 1.15 = 0.85M × 1.15 = 0.9775M. Given selling price = Rs. 1955, so 0.9775M = 1955 ⇒ M = 1955 / 0.9775 ≈ Rs. 2000. The discount is 15% of M = 0.15 × 2000 = Rs. 300. Hence, the discount amount is Rs. 300, which corresponds to option C.

Given that selling 20 toffees for 1 rupee results in a 40% loss, the cost price (CP) for 20 toffees is higher than 1 rupee. Specifically, CP = Selling Price / (1 - Loss%) = 1 / (1 - 0.40) = 1 / 0.60 = 1.6667 rupees for 20 toffees. To gain 20%, the selling price must be 1.2 times the cost price, so new selling price = 1.2 × 1.6667 = 2 rupees for 20 toffees. Therefore, for 1 rupee, the number of toffees to sell = (20 toffees) × (2 rupees / 1 rupee) = 40 toffees / 2 = 16 toffees. Hence, to gain 20%, he must sell 16 toffees for 1 rupee.

The equivalent single discount for successive discounts of 10%, 20%, and 40% is calculated as 1 - (0.9 × 0.8 × 0.6) = 1 - 0.432 = 0.568 or 56.8%.

The sale price including sales tax is Rs. 616, and the sales tax rate is 10%, so the price before tax is Rs. 616 ÷ 1.10 = Rs. 560. The shopkeeper made a 12% profit, so the cost price is Rs. 560 ÷ 1.12 = Rs. 500.

Samad bought 20 dozens (240 toys) at Rs. 375 per dozen, so total cost = 20 × 375 = Rs. 7500. He sold each toy at Rs. 33, so total revenue = 240 × 33 = Rs. 7920. Profit = 7920 - 7500 = Rs. 420. Percentage profit = (420 / 7500) × 100 = 5.6%. However, the calculation shows 5.6%, which matches option C, but rechecking the math: 20 dozens = 240 toys; cost price per toy = 375/12 = 31.25; total cost = 31.25 × 240 = 7500; selling price per toy = 33; profit per toy = 1.75; total profit = 1.75 × 240 = 420; percentage profit = (420/7500)×100 = 5.6%. So the correct answer is C, not D. The initial explanation was incorrect. Therefore, correct answer is C.

The man sold 20 articles for Rs. 60 and gained 20%. This means the selling price (SP) of 20 articles is Rs. 60, and the gain is 20%. To find the cost price (CP) of 20 articles, use the formula SP = 1.2 × CP (since gain is 20%). Thus, CP = 60 / 1.2 = Rs. 50 for 20 articles. The cost price per article is Rs. 50 / 20 = Rs. 2.5. With Rs. 60, the number of articles he can buy is 60 / 2.5 = 24 articles. Therefore, the correct answer is option B (24 articles).

The cost price (CP) is 64% of the marked price (MP), so CP = 0.64 MP. A discount of 12% on MP means selling price (SP) = 0.88 MP. Gain = SP - CP = 0.88 MP - 0.64 MP = 0.24 MP. Gain percent = (Gain/CP) × 100 = (0.24 MP / 0.64 MP) × 100 = 37.5%.

The cost price (CP) of 70 kg of potatoes is Rs. 420, so the cost price per kg is Rs. 420 ÷ 70 = Rs. 6. The selling price (SP) per kg is Rs. 6.50. The total selling price is 70 × 6.50 = Rs. 455. The gain is SP - CP = Rs. 455 - Rs. 420 = Rs. 35. The gain percent is (Gain / CP) × 100 = (35 / 420) × 100 = 8.33%, which is 8 1/3%. Therefore, the correct answer is option C.