# Problems on Trains Quiz Set 011

### Question 1

A train of length 74m is running at a speed of 61m/s. How long will it take to cross a tunnel of length 48m?

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 \${74 + 48}/61\$ = 2s.

### Question 2

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 288m, and the sum of their speeds is 48m/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 = 288. This distance has to be covered at a net relative speed equal to the sums of the speeds of the two trains, so v = 48. The time will be distance/speed = \$288/48\$ = 6 sec.

### Question 3

A train running at 10km/h leaves a railway station 45 hours later than another train, and meets it in 5 hours. What is the speed of the other train?

A

1 km/h.

B

2 km/h.

C

4 km/h.

D

3 km/h.

Soln.
Ans: a

Let the speed of the train be v km/h. Distance travelled by this train in (5 + 45) hours = 50v km. Equating this to the distance travelled by the second train we get 50v = 10 × 5, which gives v = 1 km/h.

### Question 4

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 5

A train is moving at a speed of 70m/s. It takes 2 seconds to cross a jeep that is travelling in the opposite direction at a speed of 31m/s. What is the length of the train?

A

202 meters.

B

203 meters.

C

201 meters.

D

204 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 = 70 + 31 = 101. The length of the train will be time × speed = \$2 × 101\$ = 202meters. 