# Problems on Trains Quiz Set 015

### Question 1

Two trains moving in the same direction, and running respectively at 36km/h and 72km/h cross each other in 7sec. What is the length of each train if the two trains are equally long?

A

35 m.

B

36 m.

C

34 m.

D

37 m.

Soln.
Ans: a

The trains cover a distance equal to the sum of their lengths at a relative speed 72 - 36 = 36km/h × (5/18), or 10m/s. We can use the speed distance formula: sum of lengths = 10 × 7 = 70m. Halving this we get the length of one train = 35m.

### Question 2

A train takes 3 hours less if its speed is increased by 2 km/hr. What is the normal speed if the distance is 12km?

A

2.

B

3.

C

5.

D

4.

Soln.
Ans: a

Let the normal speed be x km/hr. We have been given \$12/x\$ - \$12/{x + 2}\$ = 3. This translates to the quadratic equation \$3x^2 + 6x - 24 = 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.

### Question 3

A train of length 107m is running at a speed of 38m/s. How long will it take to cross a tunnel of length 45m?

A

4 sec.

B

5 sec.

C

3 sec.

D

6 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 \${107 + 45}/38\$ = 4s.

### Question 4

A train running at a speed of 18m/s crosses a pole in 16sec. How long will it take to cross a platform of length 864m?

A

64 sec.

B

65 sec.

C

63 sec.

D

66 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 = \$18 × 16\$ = 288m. 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 = \${288 + 864}/18\$ = 64 seconds.

### Question 5

A train is moving at a speed of 63m/s. It takes 8 seconds to cross a jeep that is travelling in the opposite direction at a speed of 70m/s. What is the length of the train?

A

1064 meters.

B

1065 meters.

C

1063 meters.

D

1066 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 = 63 + 70 = 133. The length of the train will be time × speed = \$8 × 133\$ = 1064meters. 