The speed of train A is 20 m/sec, which is double the speed of train B. The ratio of the length of the trains A to B is 10:7, respectively. Train B can cross a pole in 28 seconds; then find the length of train A (in meters).

The correct answer is 400 meters.

Let us work through this problem step by step using the given information.

Step 1: Find the speed of Train B

We are told that the speed of Train A is 20 m/sec, and this is double the speed of Train B. Therefore:

Speed of Train B = \frac{20}{2} = 10 m/sec

Step 2: Find the length of Train B using the pole-crossing condition

When a train crosses a pole (a stationary point object with negligible width), the distance covered equals the length of the train itself. Train B crosses a pole in 28 seconds at a speed of 10 m/sec. So:

Length of Train B = Speed × Time

Length of Train B = 10\times 28 = 280 meters

Step 3: Find the length of Train A using the ratio

The ratio of the length of Train A to Train B is given as 10 : 7. Using this ratio:

\frac{\text{Length of Train A}}{\text{Length of Train B}}=\frac{10}{7}

\text{Length of Train A}=\frac{10}{7}\times 280

\text{Length of Train A}=10\times 40=400\text{meters}

Summary of key steps:
- Speed of B = 20 �� 2 = 10 m/sec
- Length of B = 10 × 28 = 280 m
- Length of A = (10/7) × 280 = 400 m

The length of Train A is 400 meters.