# Problems on Trains Quiz Set 006

### Question 1

Two trains moving in the same direction, and running respectively at 72km/h and 144km/h cross each other in 5sec. What is the length of each train if the two trains are equally long?

A

50 m.

B

51 m.

C

49 m.

D

52 m.

Soln.
Ans: a

The trains cover a distance equal to the sum of their lengths at a relative speed 144 - 72 = 72km/h × (5/18), or 20m/s. We can use the speed distance formula: sum of lengths = 20 × 5 = 100m. Halving this we get the length of one train = 50m.

### Question 2

A train of length 73m is running at a speed of 57m/s. How long will it take to cross a tunnel of length 41m?

A

2 sec.

B

3 sec.

C

5 sec.

D

4 sec.

Soln.
Ans: a

The total distance to be covered is equal to the length of the train plus the length of the tunnel. By the time and distance formula, we get time = distance/speed, which gives \${73 + 41}/57\$ = 2s.

### Question 3

Two equally long trains of length 90m cross each other in 6sec. If one train is twice as fast as the other, then what is the speed of the faster train?

A

72 km/h.

B

73 km/h.

C

71 km/h.

D

74 km/h.

Soln.
Ans: a

Let the speeds be v and 2v. The trains cover a distance equal to the sum of their lengths at a relative speed v + 2v = 3v. We can use the speed distance formula: \$3v = {90 + 90}/6\$, which gives v = \${180/{3 × 6}} × (18/5)\$ = 36km/h. So the speed of the faster train is twice = 72km/h.

### Question 4

A train of length 129 m crosses a bridge at a speed of 60 km/h in 30 seconds. What is the length of the bridge?

A

371 meters.

B

500 meters.

C

450 meters.

D

600 meters.

Soln.
Ans: a

In 30 seconds the train covers a distance of 30 × 60 × (5/18) = 500 meters. This distance is the sum of the lengths of the train and the bridge. Subtracting the length of the train we get the length of the bridge = 500 - 129 = 371 meters.

### Question 5

Two trains are moving in same direction on two parallel tracks. How many seconds will they take to cross each other if the sum of their lengths is 306m, and the difference of their speeds is 51m/s?

A

6 sec.

B

7 sec.

C

5 sec.

D

8 sec.

Soln.
Ans: a

The total distance is equal to the sum of the lengths of the trains, so s = 306. This distance has to be covered at a net relative speed equal to the difference of the speeds of the two trains, so v = 51. The time will be distance/speed = \$306/51\$ = 6s. 