Problems on Trains Quiz Set 002

Question 1

Two trains coming from opposite direction and running respectively at 60km/h and 120km/h cross each other in 5sec. What is the length of each train if the two trains are equal?

A

125 m.

B

126 m.

C

124 m.

D

127 m.

Soln.
Ans: a

The trains cover a distance equal to the sum of their lengths at a relative speed 60 + 120 = 180km/h × (5/18), or 50m/s. We can use the speed distance formula: sum of lengths = 50 × 5 = 250m. Halving this we get the length of one train = 125m.

Question 2

A train is moving at a speed of 87m/s. It takes 3 seconds to cross a jeep that is travelling in the opposite direction at a speed of 76m/s. What is the length of the train?

A

489 meters.

B

490 meters.

C

488 meters.

D

491 meters.

Soln.
Ans: a

The distance to be covered is equal to the length of the train. This distance has to be covered at a net relative speed equal to the sums of the speeds of the jeep and the train, so v = 87 + 76 = 163. The length of the train will be time × speed = \$3 × 163\$ = 489meters.

Question 3

A train of length 228m crosses a pole in 19 sec. How long will it take to cross a platform of length 456 m?

A

57 sec.

B

58 sec.

C

56 sec.

D

59 sec.

Soln.
Ans: a

The speed of the train can be obtained from the time it takes to cross the pole. The speed = \$228/19\$ = 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 = \${228 + 456}/12\$ = 57seconds.

Question 4

A train running at a speed of 17m/s crosses a pole in 13sec. How long will it take to cross a platform of length 1105m?

A

78 sec.

B

79 sec.

C

77 sec.

D

80 sec.

Soln.
Ans: a

The length of the train can be obtained from the time it takes to cross the pole. The length of the train = \$17 × 13\$ = 221m. 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 = \${221 + 1105}/17\$ = 78 seconds.

Question 5

A train is moving at a speed of 60m/s. It takes 5 seconds to cross a jeep that is travelling in the opposite direction at a speed of 76m/s. What is the length of the train?

A

680 meters.

B

681 meters.

C

679 meters.

D

682 meters.

Soln.
Ans: a

The distance to be covered is equal to the length of the train. This distance has to be covered at a net relative speed equal to the sums of the speeds of the jeep and the train, so v = 60 + 76 = 136. The length of the train will be time × speed = \$5 × 136\$ = 680meters.