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).

Correct Answer: 400

Let us solve the problem step-by-step:

Step 1: Determine the speed of train B.
We are given that the speed of train A is 20 m/sec, which is double the speed of train B.
Therefore, the speed of train B is:
Speed of train B = (Speed of train A) / 2
Speed of train B = 20 / 2 = 10 m/sec

Step 2: Find the length of train B.
Train B crosses a pole in 28 seconds. When a train crosses a pole, the distance traveled by the train is equal to its own length.
Length of train B = Speed of train B × Time taken to cross the pole
Length of train B = 10 m/sec × 28 seconds = 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 10:7.
Let the length of train A be 10x and the length of train B be 7x.
Since the length of train B is 280 meters, we have:

$7x=280$

Solving for x:

$x=\frac{280}{7}=40$

Now, find the length of train A:
Length of train A = 10x = 10 × 40 = 400 meters

Thus, the length of train A is 400 meters.