Question

A train running at the speed of 72 km/hr can cross a stationary pole in 10 seconds. How much time will it take to overtake a train of length 500 metres running at 54 km/hr in the same direction?

• A. 130 seconds
• B. 110 seconds
• C. 120 seconds
• D. 140 seconds

Answer 1

The Correct Option is D

Train Overtaking Calculation 

- The speed of the first train is 72 km/hr and it crosses a stationary pole in 10 seconds. The length of the first train can be calculated using the formula:

\[ \text{Speed} = \frac{\text{Distance}}{\text{Time}} \]

- Converting the speed from km/hr to m/s:

\[ 72 \text{ km/hr} = \frac{72 \times 1000}{3600} = 20 \text{ m/s} \]

- The length of the train is:

\[ \text{Length of the train} = \text{Speed} \times \text{Time} = 20 \times 10 = 200 \text{ metres} \]

- Now, we need to calculate the time it will take for this 200-metre train to overtake another train moving at 54 km/hr.

- Converting the speed of the second train to m/s:

\[ 54 \text{ km/hr} = \frac{54 \times 1000}{3600} = 15 \text{ m/s} \]

- The relative speed of the two trains when moving in the same direction is:

\[ \text{Relative Speed} = 20 \text{ m/s} - 15 \text{ m/s} = 5 \text{ m/s} \]

- The total distance to be covered while overtaking is the length of the first train plus the length of the second train:

\[ \text{Total Distance} = 200 \text{ metres} + 500 \text{ metres} = 700 \text{ metres} \]

- The time required to overtake is:

\[ \text{Time} = \frac{\text{Total Distance}}{\text{Relative Speed}} = \frac{700}{5} = 140 \text{ seconds} \]

Conclusion: The time it will take to overtake the second train is 140 seconds.