# Problems on Trains Quiz Set 007

### 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?

A

416 meters.

B

417 meters.

C

415 meters.

D

418 meters.

Soln.
Ans: a

The total distance to be covered is equal to the length of the train. By the time and distance formula, we get length = time × speed, which gives \$8 × 52\$ = 416m.

### 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.