Question

Three trains P, Q and R are of lengths 1800 m, 2100 m and 2400 m respectively. P and R cross each travelling in opposite direction in 70 seconds. Q and R cross each travelling in opposite direction in 450/13 seconds. What is the difference in the speeds of trains P and Q?
1. 24
2. 19
3. 20
4. 23

Answer 1

Correct Answer - Option 3 : 20

Given:

Three trains P, Q and R are of lengths 1800 m, 2100 m and 2400 m respectively. P and R cross each travelling in opposite direction in 70 seconds. Q and R cross each travelling in opposite

direction in 450/13 seconds.

Formula:

If the lengths of two trains are a and b,

Time taken to cross each other when travelling in same direction = (a + b)/(va - vb)

Time taken to cross each other when travelling in opposite direction = (a + b)/(va + vb)

where va and vb are the speeds of trains A and B respectively.

Calculation:

Let speeds of P, Q and R be p, q and r respectively.

⇒ (1800 + 2400)/(p + r) = 70

⇒ (2100 + 2400)/(q + r) = 450/13

⇒ p + r = 150

⇒ q + r = 130

⇒ r = 150 – p

⇒ r = 130 – q
⇒ p – r = 20