# Problems on Trains Quiz Set 001

### Question 1

A train is running at a speed of 89m/s. If it takes 6sec to move past a telegraph pole, then what is its length?

A

534 meters.

B

535 meters.

C

533 meters.

D

536 meters.

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 length = time × speed, which gives \$6 × 89\$ = 534m.

### Question 2

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 3

A train speeding at 18 km/h crosses the platform in 48seconds, but it takes 5 seconds to cross a man standing on the same platform. What is the length of the train?

A

215 meters.

B

216 meters.

C

214 meters.

D

217 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 × 5\$ = 25meters. The combined length of the train and platform can be obtained from the time it takes to cross the platform, = \$5 × 48 = 240\$ meters. Subtracting, we get the length of the train = 215 m.

### Question 4

A train speeding at 18 km/h crosses the platform in 56seconds, but it takes 7 seconds to cross a man standing on the same platform. What is the length of the train?

A

245 meters.

B

246 meters.

C

244 meters.

D

247 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 × 7\$ = 35meters. The combined length of the train and platform can be obtained from the time it takes to cross the platform, = \$5 × 56 = 280\$ meters. Subtracting, we get the length of the train = 245 m.

### Question 5

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.