# Problems on Trains Quiz Set 018

### Question 1

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.

### Question 2

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 3

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?

A

3204 meters.

B

3205 meters.

C

3203 meters.

D

3206 meters.

Soln.
Ans: a

In 23 seconds the train covers a distance of 23 × 40 × (18/5) = 3312 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 = 3312 - 108 = 3204 meters.

### Question 4

Two trains moving in the same direction, and running respectively at 72km/h and 144km/h cross each other in 14sec. What is the length of each train if the two trains are equally long?

A

140 m.

B

141 m.

C

139 m.

D

142 m.

Soln.
Ans: a

The trains cover a distance equal to the sum of their lengths at a relative speed 144 - 72 = 72km/h × (5/18), or 20m/s. We can use the speed distance formula: sum of lengths = 20 × 14 = 280m. Halving this we get the length of one train = 140m.

### Question 5

Two trains moving in the same direction, and running respectively at 72km/h and 144km/h cross each other in 5sec. What is the length of each train if the two trains are equally long?

A

50 m.

B

51 m.

C

49 m.

D

52 m.

Soln.
Ans: a

The trains cover a distance equal to the sum of their lengths at a relative speed 144 - 72 = 72km/h × (5/18), or 20m/s. We can use the speed distance formula: sum of lengths = 20 × 5 = 100m. Halving this we get the length of one train = 50m.