Question

A train x running at 74 km/h crosses another train y running at 52 km/h in the opposite direction in 12 seconds. If the length of y is two-thirds that of x, then what is the length of y (in m) ?

1. 210
2. 200
3. 168
4. 252

Answer 1

Correct Answer - Option 3 : 168

Given:

Speed of train x = 74 km/h

Speed of train y = 52 km/h

Train x crosses train y in opposite direction in 12 seconds.

Length of train y = 2/3 of length of train x

Concept used:

(i) If speed of body A is x and speed of body B is y then, Relative speed of two bodies moving in opposite direction = (x + y)

(ii) 1 km/h = 5/18 m/s

Formula used:

Relative speed = Total length/Time taken to cross

Calculations:

Relative speed = Total length/Time taken to cross

⇒ (74 + 52)(5/18) = Total length/12

⇒ (126)(5/18) = Total length/12

⇒ Total length = 35 × 12

⇒ Total length = 420 m

Let the length of train x be 3a.

So, length of train y = 2/3 × 3a = 2a

⇒ 2a + 3a = 420

⇒ 5a = 420

⇒ a = 84

Length of train y = 2a

= 2 × 84

= 168 m

∴ The length of train y is 168 m.