Mathematics

The train's speed is 240 m / 24 s = 10 m/s. To pass a platform 650 m long, the train must cover 240 + 650 = 890 m. Time taken = 890 m / 10 m/s = 89 seconds, which rounds to 89 seconds. However, option B is 89 Sec, so the correct answer is B, not C. Rechecking: 890/10=89 seconds exactly, so correct answer is B.

Given that 25 men consume 250 kg of wheat in 20 days, the total man-days is 25 × 20 = 500 man-days. The wheat consumption per man-day is 250 kg ÷ 500 = 0.5 kg. For 20 men over 25 days, the total man-days is 20 × 25 = 500 man-days. Therefore, the total wheat consumed is 500 × 0.5 = 250 kg. Hence, the correct answer is 250 kg, which corresponds to option C.

Initially, food is sufficient for 600 men for 30 days, so total man-days of food = 600 × 30 = 18,000. When 400 more men arrive, total men = 1000. The food will last 18,000 ÷ 1000 = 18 days. However, the options given are 20, 18, 28, and 36 days. The correct calculation shows 18 days, so the correct answer is B, not A. Therefore, the original correct_answer 'B' is correct. The explanation was missing and has been added.

Let the first sum be x and the second sum be y. Given that (1/4)x = (1/5)y, so 5x = 4y or y = (5/4)x. Interest from first sum for 2 years = x * 6% * 2 = 0.12x. Interest from second sum for 2 years = y * 7% * 2 = 0.14y = 0.14 * (5/4)x = 0.175x. Total interest = 0.12x + 0.175x = 0.295x = 354. Solving for x gives x = 354 / 0.295 = 1200. Then y = (5/4)*1200 = 1500. Total sum = x + y = 1200 + 1500 = Rs.2700.

The deposit is 10% of $21,000, which is $2,100. The balance to be financed is $18,900. Interest at 12% per annum on the reducing balance over 60 months results in a monthly installment of approximately $504, matching option B.

The difference in interest for 3 years at 2% higher rate is Rs.360. Using the formula for simple interest difference: Principal × Rate difference × Time / 100 = 360. Substituting time = 3 years and rate difference = 2%, we get Principal = (360 × 100) / (2 × 3) = Rs.6000.

The marked price is Rs. 880. After a 20% discount, the selling price = 880 - 20% of 880 = 880 - 176 = Rs. 704. Since the shopkeeper earns a 10% profit, cost price = selling price / 1.10 = 704 / 1.10 = Rs. 640. However, Rs. 640 is option B, so let's recheck calculations carefully: Selling price = 880 × 0.8 = 704; Cost price = Selling price / 1.10 = 704 / 1.10 = 640. Thus, the cost price is Rs. 640 (option B). The original correct_answer was C (Rs. 774), which is incorrect. The correct answer is B (Rs. 640).

The difference in amount over 3 years (from year 5 to year 8) is Rs. 12005 - Rs. 9800 = Rs. 2205, which is the simple interest for 3 years. Therefore, the interest for 1 year is Rs. 2205 / 3 = Rs. 735. The principal amount is Rs. 9800 - (5 × 735) = Rs. 9800 - 3675 = Rs. 6125. The rate of interest per annum is (Interest per year / Principal) × 100 = (735 / 6125) × 100 ≈ 12%. However, this contradicts the options, so let's re-examine: Actually, the principal is unknown, so let's calculate the interest per year as Rs. 2205 / 3 = Rs. 735. The interest for 5 years is Rs. 9800 - P, and for 8 years is Rs. 12005 - P. The difference is Rs. 2205, which is 3 years interest, so yearly interest = Rs. 735. Therefore, 5 years interest = 5 × 735 = Rs. 3675. So principal P = Rs. 9800 - 3675 = Rs. 6125. Rate = (Interest per year / Principal) × 100 = (735 / 6125) × 100 ≈ 12%. So the correct rate is 12%, which corresponds to option C. Therefore, the original correct answer C is correct. The initial confusion was in the explanation steps, but the final calculation confirms 12%.

The man buys the watch for Rs. 1950 and sells it on credit for Rs. 2200 payable after 1 year. The present value of Rs. 2200 due after 1 year at 10% interest is 2200 / 1.10 = Rs. 2000. Since he effectively receives Rs. 2000 now for an item costing Rs. 1950, his gain is Rs. 2000 - Rs. 1950 = Rs. 50. However, the gain options are Rs. 55, Rs. 50, Rs. 30, and loss Rs. 30. Rechecking the calculation: The gain is the difference between the present value of the selling price and the cost price. Present value = 2200 / (1 + 0.10) = 2000. Gain = 2000 - 1950 = Rs. 50. So the correct gain is Rs. 50, which corresponds to option B. Therefore, the original correct_answer B is correct. The explanation is now added to clarify this.

First, find the daily food consumption per chicken: 5 kg for 50 chickens in 2 days means 5 kg / 2 days = 2.5 kg per day for 50 chickens, so per chicken per day is 2.5 kg / 50 = 0.05 kg. For 60 chickens in 6 days: 60 * 6 * 0.05 = 18 kg.