# Problems on Trains Quiz Set 010

### Question 1

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 platform?

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 platform= 180 m.

### Question 2

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.

### Question 3

A train of length 656m is running at a speed of 82m/s. How long will it take to cross a pole standing alongside the track?

A

8 sec.

B

9 sec.

C

7 sec.

D

10 sec.

Soln.
Ans: a

The total distance to be covered is equal to the length of the train. By the time and distance formula, we get time = distance/speed, which gives \$656/82\$ = 8s.

### Question 4

Two trains running in opposite directions cross each other in 32 seconds. They, respectively, take 16 and 69 seconds to cross a man standing on the platform. What is the ratio of their speeds?

A

\${16/37}\$.

B

\$1{17/36}\$.

C

\$2{4/13}\$.

D

\$3{10/39}\$.

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 × 16) + (rv × 69)\$ which should equal the value obtained from the time they take to cross each other,i.e., \$(v + rv) × 32)\$. So \$v × (16 + r × 69\$ = \$v × (1 + r) × 32).\$ Cancelling v and solving for r we get \${16/37}\$.

### Question 5

A train of length 315m is running at a speed of 45m/s. How long will it take to cross a pole standing alongside the track?

A

7 sec.

B

8 sec.

C

6 sec.

D

9 sec.

Soln.
Ans: a

The total distance to be covered is equal to the length of the train. By the time and distance formula, we get time = distance/speed, which gives \$315/45\$ = 7s.