Profit, Loss and Discount

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.

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.

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.

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.

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.

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 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.

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.

Kamal invested Rs. 9000 for 12 months, so his capital-time product is 9000 × 12 = 108000. Sameer invested Rs. 8000 for 7 months, so his capital-time product is 8000 × 7 = 56000. The total capital-time product is 108000 + 56000 = 164000. Sameer's share of profit = (56000 / 164000) × 6970 ≈ Rs. 2380. However, this matches option B, but the calculation shows option B is correct. Rechecking: 56000/164000 = 0.34146; 0.34146 × 6970 = 2380. So option B is correct. The initial explanation was incorrect. Therefore, the correct answer is B.

The profit shares of partners A, B, and C are proportional to their capitals. The capitals are Rs. 8000, Rs. 10000, and Rs. 12000 respectively, so the ratio of their capitals (and hence profit shares) is 8:10:12. Given B's profit share is Rs. 1500, each share corresponds to Rs. 150 (1500 ÷ 10). Therefore, A's share is 8 × 150 = Rs. 1200 and C's share is 12 × 150 = Rs. 1800. The difference between A and C's profit shares is Rs. 1800 - Rs. 1200 = Rs. 600. Among the options given (Rs. 300, Rs. 400, Rs. 500, Rs. 600), the correct difference is Rs. 600, which corresponds to option D.

The profit share is proportional to the product of investment and time. A invested Rs.25000 for 12 months, B Rs.30000 for 12 months, and C Rs.35000 for 8 months (since C joined after 4 months). Calculating shares: A=25000*12=300000, B=30000*12=360000, C=35000*8=280000. Total=940000. C's share = (280000/940000)*47000 ≈ Rs.14000. However, the calculation shows Rs.14000, which matches option D, so the original answer D is correct. Rechecking calculations: 280000/940000=0.2979; 0.2979*47000=13999 ≈ Rs.14000. So the original answer D is correct. The initial explanation was missing, so it has been added.

A invests Rs.1200 for 12 months, so his investment-months = 1200 × 12 = 14400. B joins after 3 months, so B's investment is for 9 months. Let B's investment be x, so investment-months = 9x. C joins after 6 months, so C's investment is for 6 months. Let C's investment be y, so investment-months = 6y. The profit ratio 2:3:5 corresponds to the investment-months ratio 14400 : 9x : 6y = 2 : 3 : 5. From 14400/2 = 9x/3 = 6y/5, we get 14400/2 = 7200, so 9x/3 = 7200 which gives 3x = 7200, hence x = 2400. Therefore, B's investment is Rs.2400, which corresponds to option A.

A's share of profit is 2/3. The increase in profit rate from 5% to 7% causes A's income to increase by Rs.200, which corresponds to 2% of A's capital share. Calculating A's capital from this, then using profit shares to find B's capital, we find B's capital is Rs.3600.

The profit sharing ratio in a partnership depends on the product of the capital invested and the time for which it is invested. Here, A invests Rs. 40,000 for 3 years, so the product is 40,000 × 3 = 120,000. B invests Rs. 80,000 for 1 year and then Rs. 40,000 for 2 years (after withdrawing Rs. 40,000 at the end of the first year), so the product is (80,000 × 1) + (40,000 × 2) = 80,000 + 80,000 = 160,000. C invests Rs. 1,20,000 for 2 years and then Rs. 40,000 for 1 year (after withdrawing Rs. 80,000 at the end of the second year), so the product is (1,20,000 × 2) + (40,000 × 1) = 240,000 + 40,000 = 280,000. The ratio of their investments by time is therefore 120,000 : 160,000 : 280,000, which simplifies to 12 : 16 : 28, and further to 3 : 4 : 7. This matches option B, so the correct answer is B.

P's annual salary is Rs. 5000 × 12 = Rs. 60,000. The total profit is Rs. 2,00,000. After paying P's salary, the remaining profit to be shared is Rs. 2,00,000 - Rs. 60,000 = Rs. 1,40,000. The profit is shared in the ratio of their investments, which is 4 lakhs : 10 lakhs = 2 : 5. So, P's share of the profit is (2/7) × 1,40,000 = Rs. 40,000 and Q's share is (5/7) × 1,40,000 = Rs. 1,00,000. Therefore, P's total earning = salary + profit share = 60,000 + 40,000 = Rs. 1,00,000 and Q's total earning = Rs. 1,00,000. Hence, the ratio of their earnings is 1,00,000 : 1,00,000 = 1 : 1. So, the correct answer is option D.

Sameena invested Rs. 50,000 for 3 years (36 months), while Nida joined after 6 months, so she invested Rs. 80,000 for 2.5 years (30 months). The profit sharing ratio is calculated based on the product of capital and time: (50,000 × 36) : (80,000 × 30) = 1,800,000 : 2,400,000 = 3 : 4. Total profit is Rs. 24,500, so Sameena's share = (3/7) × 24,500 = Rs. 10,500. This matches option B exactly, confirming the correct answer.

The profit shares in a partnership where investments are made for different durations are proportional to the product of the amount invested and the time period of investment. Here, A invests Rs. 10,000 for 8 months, so A's capital-time product is 10,000 × 8 = 80,000. B invests Rs. 10,000 for 12 months, so B's capital-time product is 10,000 × 12 = 120,000. The total capital-time product is 80,000 + 120,000 = 200,000. A's share of the profit is (80,000 / 200,000) × 25,000 = Rs. 10,000, and B's share is (120,000 / 200,000) × 25,000 = Rs. 15,000. This matches option D, making it the correct answer.

The profit is shared in the ratio of their investments: 22500:35000 = 9:14. Total parts = 9 + 14 = 23. Raees's share = (14/23) × 13800 = Rs. 8400.

The profit shares are proportional to the capitals. Given A's capital is Rs.5000 and his profit share is Rs.200 out of Rs.800, the ratio of A's capital to total capital is 200/800 = 1/4. Similarly, C's profit share is Rs.130, so the ratio of C's capital to total capital is 130/800 = 13/80. Using these ratios, we can find B's capital by subtracting A's and C's capitals from the total capital. Calculating B's capital gives Rs.6250.

The profit sharing ratio in a partnership where partners invest different amounts for the same duration is proportional to their capital investments. Since both P and Q invested for the same time period (2 years), the ratio of their profits will be the ratio of their investments. P invested Rs. 85,000 and Q invested Rs. 15,000, so the profit sharing ratio is 85,000 : 15,000, which simplifies to 17 : 3. Therefore, the profit earned after 2 years should be divided between P and Q in the ratio 17:3.

The profit is divided in the ratio of investments: 35,000 : 45,000 : 55,000, which simplifies to 7 : 9 : 11. The total parts are 7+9+11=27. Each part equals 40,500/27 = 1,500. Therefore, A's share = 7×1,500=10,500; B's share = 9×1,500=13,500; C's share = 11×1,500=16,500.

The profit sharing ratio depends on the product of capital invested and the time for which it was invested. A invested Rs. 40,000 for 3 years = 40,000 × 3 = 120,000; B invested Rs. 80,000 for 1 year and Rs. 40,000 for 2 years (after withdrawing 40,000) = (80,000 × 1) + (40,000 × 2) = 80,000 + 80,000 = 160,000; C invested Rs. 1,20,000 for 2 years and Rs. 40,000 for 1 year (after withdrawing 80,000) = (1,20,000 × 2) + (40,000 × 1) = 240,000 + 40,000 = 280,000. The ratio is 120,000 : 160,000 : 280,000 = 3 : 4 : 7, which corresponds to option D. However, the initial calculation here shows option D is correct, so the original correct_answer 'D' is correct. The explanation is now provided.

Profit sharing is based on the product of capital and time invested. Ameen invested for 36 months (70,000 × 36 = 2,520,000), Rahim for 30 months (105,000 × 30 = 3,150,000), and Sameer for 24 months (140,000 × 24 = 3,360,000). The ratio of their profit shares is 2,520,000 : 3,150,000 : 3,360,000, which mathematically simplifies to 12:15:16.

The profit share among partners is proportional to the product of their investment and the time period of investment. Calculating each partner's investment*time: A = 6000*5 = 30000, B = 3600*6 = 21600, C = 7500*3 = 22500. Total = 30000 + 21600 + 22500 = 74100. A's share of the profit = (30000 / 74100) * 7410 = Rs.3000. Therefore, the correct answer is Rs.3000, which corresponds to option B.

The profit ratio between two partners is proportional to the product of their investment and the time for which the investment is made. Given the investment ratio of P and Q as 7:5 and the profit ratio as 7:10, and knowing P invested for 5 months, we set up the equation: (7 × 5) : (5 × t) = 7 : 10. Simplifying, 35 : 5t = 7 : 10, which leads to 35 × 10 = 7 × 5t, so 350 = 35t, and t = 10 months. Therefore, Q invested the money for 10 months, making option B the correct answer.