Question

A 400 metres long train moves with a speed of 72 km/hr and crosses a boundary of a steel factory in 2 minutes. How much time (in seconds) would it take to cross the boundary if the boundary was 500 metres shorter?
1. 65 seconds
2. 105 seconds
3. 95 seconds
4. 85 seconds

Answer 1

Correct Answer - Option 3 : 95 seconds

Given,

Length of train = 400 metres

Time is taken to cross the boundary = 2 minutes

Speed = 72 km/hr

Formula used,

Speed of train = (length of train + length of boundary)/time taken to cross the boundary

Calculation

Length of train, a = 400 metres

Time taken to cross the boundary = 2 minutes

= 120 seconds

Speed = 72 km/hr

= 72 × (5/18) m/sec

= 20 m/sec

Let length of boundary is b metre.

Speed of train = (a + b)/time taken to cross the boundary

⇒ 20 = (400 + b)/120

⇒ 20 × 120 = 400 + b

⇒ 2400 – 400 = b

Length of boundary, b = 2000 metres

If the boundary would be 500 metres shorter, then its length would be 1500 metres.

New length of boundary = 1500 metres

Speed = 20 m/sec

Time is taken to cross-boundary = (Length of train + length of boundary)/Speed of train

⇒ Time is taken to cross-boundary = (1500 + 400)/20 = 95 seconds

∴Time is taken to cross the boundary is 95 seconds