# Problems on Trains Quiz Set 017

### Question 1

A train is running at a speed of 39m/s. If it takes 2sec to move past a telegraph pole, then what is its length?

A

78 meters.

B

79 meters.

C

77 meters.

D

80 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 \$2 × 39\$ = 78m.

### Question 2

Two equally long trains of length 50m cross each other in 5sec. If one train is twice as fast as the other, then what is the speed of the faster train?

A

48 km/h.

B

49 km/h.

C

47 km/h.

D

50 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 = {50 + 50}/5\$, which gives v = \${100/{3 × 5}} × (18/5)\$ = 24km/h. So the speed of the faster train is twice = 48km/h.

### Question 3

A train of length 285m is running at a speed of 95m/s. How long will it take to cross a pole standing alongside the track?

A

3 sec.

B

4 sec.

C

2 sec.

D

5 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 \$285/95\$ = 3s.

### 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 platform?

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 platform = 245 m.

### Question 5

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 platform?

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 platform = 215 m. 