Maths Aptitude Quiz Questions and Mock Test on Problems on Trains Set 2

Question 1

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 2

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 3

A train speeding at 18 km/h crosses the platform in 45seconds, but it takes 9 seconds to cross a man standing on the same platform. What is the length of the train?

A

180 meters.

B

181 meters.

C

179 meters.

D

182 meters.

Soln.
Ans: a

The speed of the train in m/s is 18 × (5/18) = 5 m/s. The length of the train can be obtained from the time it takes to cross the man = \$5 × 9\$ = 45meters. The combined length of the train and platform can be obtained from the time it takes to cross the platform, = \$5 × 45 = 225\$ meters. Subtracting, we get the length of the train = 180 m.

Question 4

Two trains moving in the same direction, and running respectively at 36km/h and 72km/h cross each other in 8sec. What is the length of each train if the two trains are equally long?

A

40 m.

B

41 m.

C

39 m.

D

42 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 × 8 = 80m. Halving this we get the length of one train = 40m.

Question 5

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.