# Problems on Trains Quiz Set 016

### Question 1

A train 948 meters long is moving at a speed of 95m/s. How long will it take to cross a man who is running in the opposite direction at a speed of 63m/s?

A

6 sec.

B

7 sec.

C

5 sec.

D

8 sec.

Soln.
Ans: a

The distance to be covered is equal to the length of the train, so s = 948. This distance has to be covered at a net relative speed equal to the sums of the speeds of the man and the train, so v = 95 + 63 = 158. The time will be distance/speed = \$948/158\$ = 6 s.

### 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 takes 5 hours less if its speed is increased by 12 km/hr. What is the normal speed if the distance is 120km?

A

12.

B

13.

C

11.

D

14.

Soln.
Ans: a

Let the normal speed be x km/hr. We have been given \$120/x\$ - \$120/{x + 12}\$ = 5. This translates to the quadratic equation \$5x^2 + 60x - 1440 = 0\$, which can be solved to obtain x = 12 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 4

A train 496 meters long is moving at a speed of 63m/s. How long will it take to cross a man who is running in the opposite direction at a speed of 61m/s?

A

4 sec.

B

5 sec.

C

3 sec.

D

6 sec.

Soln.
Ans: a

The distance to be covered is equal to the length of the train, so s = 496. This distance has to be covered at a net relative speed equal to the sums of the speeds of the man and the train, so v = 63 + 61 = 124. The time will be distance/speed = \$496/124\$ = 4 s.

### Question 5

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.