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### Question 1

A train is running at a speed of 52m/s. If it takes 8sec to move past a telegraph pole, then what is its length?

### Question 2

Two trains moving in the same direction, and running respectively at 36km/h and 72km/h cross each other in 7sec. What is the length of each train if the two trains are equally long?

**A**

35 m.

**B**

36 m.

**C**

34 m.

**D**

37 m.

**Soln.**

**Ans: a**

The trains cover a distance equal to the sum of their lengths at a relative speed 72 - 36 = 36km/h × (5/18), or 10m/s. We can use the speed distance formula: sum of lengths = 10 × 7 = 70m. Halving this we get the length of one train = 35m.

### Question 3

A train passes two persons walking in the same direction as the train. The time it takes to move past the man running at 2km/h is 10sec, whereas the time it takes to cross the other man running at 6km/h is 11sec. What is the speed of the train?

**A**

46 km/h.

**B**

47 km/h.

**C**

45 km/h.

**D**

48 km/h.

**Soln.**

**Ans: a**

Let the speed of the train be v km/h. Length of the train calculated with the data for the first man = $(v - 2) × 10$. It should equal the length obtained from the data for the second man. So $(v - 2) × 10$ = $(v - 6) × 11$. Please note that we have not converted seconds to hours because that factor will ultimately cancel away. Solving for v we get 46km/h.

### Question 4

A train passes two persons walking in the same direction as the train. The time it takes to move past the man running at 19km/h is 13sec, whereas the time it takes to cross the other man running at 38km/h is 14sec. What is the speed of the train?

**A**

285 km/h.

**B**

286 km/h.

**C**

284 km/h.

**D**

287 km/h.

**Soln.**

**Ans: a**

Let the speed of the train be v km/h. Length of the train calculated with the data for the first man = $(v - 19) × 13$. It should equal the length obtained from the data for the second man. So $(v - 19) × 13$ = $(v - 38) × 14$. Please note that we have not converted seconds to hours because that factor will ultimately cancel away. Solving for v we get 285km/h.

### Question 5

A train 246 meters long is moving at a speed of 61m/s. How long will it take to cross a man who is running in the opposite direction at a speed of 21m/s?

**A**

3 sec.

**B**

4 sec.

**C**

2 sec.

**D**

5 sec.

**Soln.**

**Ans: a**

The distance to be covered is equal to the length of the train, so s = 246. This distance has to be covered at a net relative speed equal to the sums of the speeds of the man and the train, so v = 61 + 21 = 82. The time will be distance/speed = $246/82$ = 3 s.

This Blog Post/Article "Problems on Trains Quiz Set 007" by Parveen (Hoven) is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.

Updated on 2017-04-07.