Question

A train overtakes two persons who are walking in the same direction in which the train is going, at the rate of 2 kmph and 4 kmph and passes them completely in 9 and 10 seconds respectively. The length of the train is:
1. 72 m
2. 54 m
3. 50 m
4. 45 m

Answer 1

Correct Answer - Option 3 : 50 m

Given:

Speed of the first person = 2 km/h

Speed of the second person = 4 km/h

Train taken to overtake the first person = 9 sec

Train taken to overtake the second person = 10 sec

Formula Used:

Speed = Distance/Time

km/h × 5/18 = m/sec

Concept used:

When two bodies move in the same direction, then

Relative speed = Difference of their speeds

Calculation:

Let the length and the speed of a train be L and V respectively.

Speed of the first person = 2 × 5/18 = 5/9 m/sec

Speed of the second person = 4 × 5/18 = 10/9 m/sec

Relative speed of the train and the first person = (V – 5/9) m/sec 

⇒ V – 5/9 = L/9 

⇒ V = L/9 + 5/9      ----(1)

Relative speed of the train and the first person = (V – 10/9) m/sec

⇒ V – 10/9 = L/10

⇒ V = L/10 + 10/9      ----(2)

Equating equation (1) and equation (2),

⇒ L/9 + 5/9 = L/10 + 10/9

⇒ L/9 – L/10 = 10/9 – 5/9

⇒ (10 × L – 9 × L)/(10 × 9) = (10 – 5)/9

⇒ (10L – 9L)/90 = 5/9

⇒ L = 5/9 × 90

⇒ L = 50 m

∴ The length of the train is 50 m.