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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 x (in m)?
1. 200
2. 168
3. 210
4. 252

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Correct Answer - Option 4 : 252

Given:

A train x running at 74 km/h crosses another train y running at 52 km/h in the opposite direction in 12 seconds. The length of y is two-thirds that of x.

Concept Used:

When two trains crossing each other, their relative speed will be the sum of their speed.

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

Distance = Time × speed

Calculation:

Relative speed (74 + 52) = 126 km/h

⇒ 126 × (5/18)

⇒ 35 m/s

Time taken to cross each other 12 second

Total distance covered (12 × 35) = 420 m

The length of y is two-thirds that of x

Let, the length of the train x is a meter

Accordingly,

(a + (2a/3) = 420    

⇒ a = 420 × (3/5)

⇒ a = 252

∴ The length of the train X is 252 m

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