# Problems on Trains Quiz Set 007

### Question 1

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 288m, and the difference of their speeds is 36m/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 = 288. This distance has to be covered at a net relative speed equal to the difference of the speeds of the two trains, so v = 36. The time will be distance/speed = \$288/36\$ = 8s.

### Question 2

A train is moving at a speed of 85m/s. It takes 7 seconds to cross a jeep that is travelling in the opposite direction at a speed of 83m/s. What is the length of the train?

A

1176 meters.

B

1177 meters.

C

1175 meters.

D

1178 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 = 85 + 83 = 168. The length of the train will be time × speed = \$7 × 168\$ = 1176meters.

### Question 3

A train running at a speed of 8m/s crosses a pole in 7sec. How long will it take to cross a platform of length 112m?

A

21 sec.

B

22 sec.

C

20 sec.

D

23 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 = \$8 × 7\$ = 56m. 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 = \${56 + 112}/8\$ = 21 seconds.

### Question 4

A train of length 108 m crosses a bridge at a speed of 40 km/h in 23 seconds. What is the length of the bridge(approx.)?

A

148 meters.

B

256 meters.

C

300 meters.

D

200 meters.

Soln.
Ans: a

In 23 seconds the train covers a distance of 23 × 40 × (5/18) = 256 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 = 256 - 108 = meters.

### Question 5

A train takes 1 hours less if its speed is increased by 4 km/hr. What is the normal speed if the distance is 3km?

A

2.

B

3.

C

5.

D

4.

Soln.
Ans: a

Let the normal speed be x km/hr. We have been given \$3/x\$ - \$3/{x + 4}\$ = 1. This translates to the quadratic equation \$1x^2 + 4x - 12 = 0\$, which can be solved to obtain x = 2 as the answer. If you don't want to solve the equation, then you can put each option into this equation and check that way. But this trick will work only if all the options have some numerical value. 