Mathematics

The total cost price (CP) of the mixture is calculated as (26 kg × Rs. 20) + (30 kg × Rs. 36) = Rs. 520 + Rs. 1080 = Rs. 1600. The total weight of the mixture is 26 + 30 = 56 kg. The selling price (SP) of the mixture is Rs. 30 per kg, so total SP = 56 × 30 = Rs. 1680. Profit = SP - CP = Rs. 1680 - Rs. 1600 = Rs. 80. Profit percent = (Profit / CP) × 100 = (80 / 1600) × 100 = 5%. Therefore, the correct profit percent is 5%, which corresponds to option B.

The machine depreciates at 20% per annum on a reducing balance basis. After two years, its value is calculated as Rs. 150,000 × (0.8)² = Rs. 96,000. To make a profit of Rs. 24,000, the selling price should be Rs. 96,000 + Rs. 24,000 = Rs. 1,20,000. This matches option B, so the correct answer is Rs. 1,20,000.

The man buys 10 articles for Rs. 8, so cost price per article = 8/10 = Rs. 0.8. He sells each at Rs. 1.25, so selling price for 10 articles = 1.25 × 10 = Rs. 12.5. Gain = 12.5 - 8 = Rs. 4.5. Gain percentage = (4.5/8) × 100 = 56.25%. Hence, the gain is 56 ¼ %.

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.

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.

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.

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.

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 angle of elevation θ can be found using tan θ = opposite/adjacent = height/shadow length = (2√3)/2 = √3. Therefore, θ = 60°.

A invests Rs. 2000 for 1 year, B invests Rs. 3000 for 2 years, and C invests Rs. 4000 for 2 years. The profit shares are proportional to the product of investment and time: A = 2000×1 = 2000, B = 3000×2 = 6000, C = 4000×2 = 8000. Total = 2000 + 6000 + 8000 = 16000. A's share of the profit = (2000/16000) × 3200 = Rs. 400. Therefore, A's share in the profit is Rs. 400, which corresponds to option D.

The profit share among partners is proportional to the product of the amount invested and the time for which it is invested. Let A's investment be x. Then B invests 2x after 6 months, so for 6 months, and C invests 3x after 8 months, so for 4 months. Calculating the weighted investments: A = x * 12 = 12x, B = 2x * 6 = 12x, C = 3x * 4 = 12x. The ratio of their investments multiplied by time is 1:1:1, so the profit is shared equally. The total profit is Rs.18,000, so A's share is one-third of Rs.18,000, which is Rs.6,000. Therefore, the correct answer is option C (Rs.6000).

Since A and B invest Rs.6000 and Rs.8000 respectively for the same duration (one year), their profit sharing ratio is directly proportional to their investments, which is 6000:8000 or 3:4.

Option B (KOMQO) is the only group where the letters do not follow a consistent alphabetical pattern or symmetry like the others. The other options have letters that form a pattern or symmetry in their positions.

Option A (27) is the only number that is not a prime number, while options B (37), C (47), and D (67) are all prime numbers. Therefore, 27 does not belong to the group.

Option B (246) is the only number composed entirely of even digits, while the others (358, 134, 862) contain at least one odd digit. Therefore, 246 does not belong to the group.

A receives 30% of the total profit as a managing partner, and the remaining 70% is divided among A, B, and C in the ratio of their capitals (5000:6000:4000). Let total profit be P. A's total profit = 0.3P + (5000/15000)*0.7P = 0.3P + (1/3)*0.7P = 0.3P + 0.2333P = 0.5333P. B's profit = (6000/15000)*0.7P = 0.28P. C's profit = (4000/15000)*0.7P = 0.1867P. Given A's profit is Rs.200 more than B's and C's combined profit: 0.5333P = 0.28P + 0.1867P + 200 => 0.5333P = 0.4667P + 200 => 0.0666P = 200 => P = 3000. Hence, total profit is Rs.3000.

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.

First, calculate the working partner A's share: 5% of Rs.7400 = Rs.370. Remaining profit = Rs.7400 - Rs.370 = Rs.7030. Calculate each partner's capital-time product: A = 6500*6=39000, B=8400*5=42000, C=10000*3=30000. Total = 39000+42000+30000=111000. C's share = (30000/111000)*7030 ≈ Rs.1900. Therefore, the correct share of C in the total profit is approximately Rs.1900, which corresponds to option B.

Both 30 and 630 are divisible by 3 and 5. 10 and 520 are divisible by 5 but not by 3. Therefore, the number that does not belong to the group based on divisibility by both 3 and 5 is 10 (option C).