Mathematics

The speed of the boat upstream is (9 - 3) = 6 km/h and downstream is (9 + 3) = 12 km/h. Let the distance between A and B be x km. The total time is given as 3 hours, so x/6 + x/12 = 3. Solving this gives x = 12 km.

The speed of the stream is calculated as half the difference between downstream and upstream speeds: (15.5 - 8.5) / 2 = 7 / 2 = 3.5 km/hr. However, option A is 3.5 km/hr, which matches this calculation, so the correct answer is A, not B. Rechecking options shows option A is 3.5 km/hr, which is correct. Therefore, correct_answer should be A.

The speed of the current is half the difference between downstream and upstream speeds: (35 - 25) / 2 = 5 kmph.

The simple interest on Rs 5000 at 10% per annum for 3 years is calculated as SI = (5000 × 10 × 3) / 100 = Rs 1500. The compound interest for the same principal, rate, and time (compounded annually) is CI = 5000 × (1 + 10/100)^3 - 5000 = 5000 × 1.331 - 5000 = Rs 1655. The difference between compound interest and simple interest is Rs 1655 - Rs 1500 = Rs 155. The closest option to Rs 155 is Rs 145 (option A), which is the best available choice among the given options.

A's simple interest for 2 years = (6000 × 5 × 2)/100 = Rs 600. B's compound interest for 2 years = 5000 × (1 + 8/100)^2 - 5000 = 5000 × 1.1664 - 5000 = Rs 832. The difference = 832 - 600 = Rs 232. However, since the question asks for the difference between their interest, the absolute difference is Rs 232, which matches option B. But the calculation shows the difference is Rs 232, so the correct answer is B, not A. Therefore, the original correct_answer is correct, but the explanation was missing and is now provided. The difficulty is easy, and tags are added accordingly.

The difference between compound interest (CI) and simple interest (SI) for 2 years at 5% per annum is given by the formula: Difference = P × (R/100)^2, where P is the principal and R is the rate of interest. Here, the difference is Rs. 1.50, and the rate R = 5%. So, 1.50 = P × (5/100)^2 = P × 0.0025. Solving for P gives P = 1.50 / 0.0025 = Rs. 600. Therefore, the sum is Rs. 600, which corresponds to option A.

The speed of the man in still water is calculated as the average of the downstream and upstream speeds: (18 + 10) / 2 = 14 kmph. The speed of the stream is half the difference between the downstream and upstream speeds: (18 - 10) / 2 = 4 kmph. Therefore, the correct answer is 14 kmph for the man in still water and 4 kmph for the stream, which corresponds to option D.

The speed of the man in still water is the average of the upstream and downstream speeds: (25 + 35) / 2 = 30 kmph. This is because the current's effect cancels out when averaging the two speeds.

Since A beats B by 22.5 m or 6 seconds in a 300 m race, B takes 6 seconds longer than A. A's speed is 300 m divided by (B's time - 6). Using the ratio of distances and times, B's time calculates to 86 seconds.

Using the compound interest formula A = P(1 + r)^t, where A = 4913, r = 6.25% = 0.0625, and t = 3 years, we solve for P: P = 4913 / (1.0625)^3 = 4913 / 1.199951 = approximately Rs. 4096. This confirms option D is correct.