Question

Two trains X and Y left point A and B simultaneously, travelling towards each other. Train X takes 9 hours and train Y takes 16 hours to reach their respective destinations after meeting. What is the total time taken by the slower train to cover the whole distance?
1. 21 hours
2. 25 hours
3. 24 hours
4. 28 hours
5. 30 hours

Answer 1

Correct Answer - Option 4 : 28 hours

Given:

Train X takes 9 hours and train Y takes 16 hours to reach their respective destinations after meeting.

Formula used:

Relation between distance and time after meeting is

S1/S2 = √(t2/t1)

Calculation:

Let the speeds of Faster and Slower cars are ‘x’ and ‘y’

Then the equation relating ratio of speed to ratio of time is

S₁/S₂ = √(t₂/t₁)

⇒ x/y = √(16/9)

⇒ x/y = 4/3

⇒ y = 3x/4

Distance covered = x × √t₁ × (√t₁ + √t₂)

⇒ Distance = x × 3 × 7 = 21x

∴ Total time taken by the slower train to cover the whole distance = 21x/ (3x/4) = 28 hours