**Problems on Trains Multiple Choice Questions**

**1. Two trains are moving in opposite directions at 60 km/hr and 90 km/hr. Their lengths are 1.2 km and 0.9 km respectively. How long will they take to cross each other?**

A. 30.2 sec

B. 40.3 sec

C. 50.4 sec

D. 60.5 sec

**Answer:** C. 50.4 sec

**Explanation: ** Since the trains are moving in opposite directions, their relative speed is (60+90) km/hr = 150 km/hr. We convert this speed from km/hr to m/sec by multiplying by 5/18, so relative speed = 150*(5/18) m/sec = 125/3 m/sec. The total distance to be covered is the sum of the lengths of the two trains, which is 1.2 km + 0.9 km = 2.1 km = 2100 m. The time they take to cross each other is Distance/Speed = 2100 m / (125/3) m/sec = 50.4 sec.

**2. A train passes a station platform in 36 seconds and a man standing on the platform in 20 seconds. If the speed of the train is 54 km/hr, what is the length of the platform?**

A. 200 m

B. 240 m

C. 280 m

D. 320 m

**Answer:** B. 240 m

**Explanation: ** The train’s speed is 54 km/hr, which is 54*(5/18) m/sec = 15 m/sec.

The length of the train is Speed * Time = 15 m/sec * 20 sec = 300 m.

When the train crosses the platform, it travels the length of the train plus the length of the platform in 36 seconds. So, 300 m + length of platform = 15 m/sec * 36 sec.

Solving for the platform’s length gives the platform’s length = 540 m – 300 m = 240 m.

**3. A train running at the speed of 60 km/hr crosses a pole in 9 seconds. What is the length of the train?**

A. 150 m

B. 120 m

C. 180 m

D. 200 m

**Answer:** A. 150 m

**Explanation: ** We know that, Distance = Speed * Time.

Here, Distance is the length of the train and time = 9 seconds.

We convert speed from km/hr to m/sec by multiplying by 5/18, so Speed = 60*(5/18) m/sec = 50/3 m/sec.

Therefore,

Distance = Speed * Time = 50/3 m/sec * 9 sec = 150 m.

So, the length of the train is 150 m.

**4. Two trains of length 110 m and 90 m are running on parallel lines in the same direction at 45 km/hr and 30 km/hr respectively. In what time will the first train pass the second train?**

A. 28 sec

B. 36 sec

C. 42 sec

D. 48 sec

**Answer:** D. 48 sec

**Explanation: ** The trains are moving in the same direction, so their relative speed is (45-30) km/hr = 15 km/hr. We convert this speed from km/hr to m/sec by multiplying by 5/18, so relative speed = 15*(5/18) m/sec = 25/6 m/sec. The first train will have to cover a distance equal to the sum of the lengths of the two trains to pass the second train completely, which is 110 m + 90 m = 200 m. So, the time taken = Distance/Speed = 200 m / (25/6) m/sec = 48 sec.

**5. A train 240 m long passed a pole in 24 sec. How long will it take to pass a platform 650 m long?**

A. 89 sec

B. 90 sec

C. 91 sec

D. 92 sec

**Answer:** A. 89 sec

**Explanation: ** The speed of the train is Distance/Time = 240 m / 24 sec = 10 m/sec. When the train crosses the platform, it travels the length of the train plus the length of the platform. So, the total distance = 240 m + 650 m = 890 m. Therefore, the time taken to cross the platform = Distance/Speed = 890 m / 10 m/sec = 89 sec.