# Problems on Trains Quiz Set 016

### Question 1

A train is running at a speed of 118km/h. If it takes 27sec to move past a telegraph pole, then what is its length?

A

885 meters.

B

886 meters.

C

884 meters.

D

887 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 × (5/18), which gives \$27 × 118 × (5/18)\$ = 885m. Please note that 5/18 is the conversion from km/h to m/s.

### Question 2

A train 948 meters long is moving at a speed of 95m/s. How long will it take to cross a man who is running in the opposite direction at a speed of 63m/s?

A

6 sec.

B

7 sec.

C

5 sec.

D

8 sec.

Soln.
Ans: a

The distance to be covered is equal to the length of the train, so s = 948. 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 = 95 + 63 = 158. The time will be distance/speed = \$948/158\$ = 6 s.

### Question 3

Two trains are moving in opposite directions on two parallel tracks. How many seconds will they take to cross each other if the sum of their lengths is 320m, and the sum of their speeds is 40m/s.?

A

8 sec.

B

9 sec.

C

7 sec.

D

10 sec.

Soln.
Ans: a

The total distance is equal to the sum of the lengths of the trains, so s = 320. This distance has to be covered at a net relative speed equal to the sums of the speeds of the two trains, so v = 40. The time will be distance/speed = \$320/40\$ = 8 sec.

### Question 4

A train 496 meters long is moving at a speed of 63m/s. How long will it take to cross a man who is running in the opposite direction at a speed of 61m/s?

A

4 sec.

B

5 sec.

C

3 sec.

D

6 sec.

Soln.
Ans: a

The distance to be covered is equal to the length of the train, so s = 496. 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 = 63 + 61 = 124. The time will be distance/speed = \$496/124\$ = 4 s.

### Question 5

A train of length 96m crosses a pole in 8 sec. How long will it take to cross a platform of length 288 m?

A

32 sec.

B

33 sec.

C

31 sec.

D

34 sec.

Soln.
Ans: a

The speed of the train can be obtained from the time it takes to cross the pole. The speed = \$96/8\$ = 12 m/s. To cross the platform it must travel a total distance equal to the combined lengths of the train and the platform at this speed. So time = \${96 + 288}/12\$ = 32seconds.