Question

A train A running at 63 km/hr passes a tunnel in 24 second, while train B running at 54 km/hr crossed a platform in 38 seconds. The ratio of the length of train A and train B is 4 : 5 and the ratio of the length of tunnel and platform is 2 : 3. What is the length of the train A?

1. 180 m
2. 200 m
3. 240 m
4. 250 m
5. 540 m

Answer 1

Correct Answer - Option 3 : 240 m

Given:

Speed of train A = 63 km/hr

Time taken by Train A to cross tunnel = 24 seconds

Speed of train B = 54 km/hr

Time taken by Train B to cross platform = 38 seconds

Ratio of the length of train A and train B = 4 : 5

Ratio of the tunnel and platform = 2 : 3

Formula Used:

Distance = Speed × Time

Calculation:

Suppose the length of train A and train B is 4x and 5x, respectively.

The length of tunnel and platform is 2y and 3y, respectively.

Distance = Speed × Time

Case I:

(4x + 2y) = 63 × 5/18 × 24

⇒ (4x + 2y) = 420      ----(i)

Case II:

(5x + 3y) = 54 × 5/18 × 38

⇒ 5x + 3y = 570      ----(ii)

Solving eq. (i) and (ii), we have –

12x + 6y = 1260      ----(iii)

10x + 6y = 1140      ----(iv)

Subtract eq. (iii) from eq. (iv), we have - 

⇒ 12x + 6y – 10x – 6y = 1260 – 1140

⇒ 2x = 120

⇒ x = 60

The length of the train A is 4x = 240 m

∴ length of train A is 240 m.