# Problems on Trains Quiz Set 013

### Question 1

A train takes 2 hours less if its speed is increased by 2 km/hr. What is the normal speed if the distance is 15km?

A

3.

B

4.

C

2.

D

5.

Soln.
Ans: a

Let the normal speed be x km/hr. We have been given \$15/x\$ - \$15/{x + 2}\$ = 2. This translates to the quadratic equation \$2x^2 + 4x - 30 = 0\$, which can be solved to obtain x = 3 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

A train passes two persons walking in the same direction as the train. The time it takes to move past the man running at 30km/h is 8sec, whereas the time it takes to cross the other man running at 34km/h is 9sec. What is the speed of the train?

A

66 km/h.

B

67 km/h.

C

65 km/h.

D

68 km/h.

Soln.
Ans: a

Let the speed of the train be v km/h. Length of the train calculated with the data for the first man = \$(v - 30) × 8\$. It should equal the length obtained from the data for the second man. So \$(v - 30) × 8\$ = \$(v - 34) × 9\$. Please note that we have not converted seconds to hours because that factor will ultimately cancel away. Solving for v we get 66km/h.

### Question 3

Two trains running in opposite directions cross each other in 26 seconds. They, respectively, take 8 and 47 seconds to cross a man standing on the platform. What is the ratio of their speeds?

A

\${6/7}\$.

B

\$2{1/6}\$.

C

\$2{2/9}\$.

D

3.

Soln.
Ans: a

Let the ratio of their speeds by r. If the speed of one train is v, then the speed of the other is rv. By the speed and distance formula, the sum of their lengths is \$(v × 8) + (rv × 47)\$ which should equal the value obtained from the time they take to cross each other,i.e., \$(v + rv) × 26)\$. So \$v × (8 + r × 47\$ = \$v × (1 + r) × 26).\$ Cancelling v and solving for r we get \${6/7}\$.

### Question 4

A train passes two persons walking in the same direction as the train. The time it takes to move past the man running at 2km/h is 10sec, whereas the time it takes to cross the other man running at 6km/h is 11sec. What is the speed of the train?

A

46 km/h.

B

47 km/h.

C

45 km/h.

D

48 km/h.

Soln.
Ans: a

Let the speed of the train be v km/h. Length of the train calculated with the data for the first man = \$(v - 2) × 10\$. It should equal the length obtained from the data for the second man. So \$(v - 2) × 10\$ = \$(v - 6) × 11\$. Please note that we have not converted seconds to hours because that factor will ultimately cancel away. Solving for v we get 46km/h.

### Question 5

A train of length 190 m crosses a bridge at a speed of 45 km/h in 21 seconds. What is the length of the bridge?

A

72.5 meters.

B

60 meters.

C

262.5 meters.

D

150 meters.

Soln.
Ans: a

In 21 seconds the train covers a distance of 21 × 45 × (5/18) = 262.5 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 = 262.5 - 190 = 72.5 meters. This Blog Post/Article "Problems on Trains Quiz Set 013" by Parveen (Hoven) is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.
Updated on 2020-02-07. Published on: 2016-05-13