# Problems on Trains Quiz Set 005

### 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 train?

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 train = 180 m.

### Question 2

A train of length 77m crosses a pole in 7 sec. How long will it take to cross a platform of length 616 m?

A

63 sec.

B

64 sec.

C

62 sec.

D

65 sec.

Soln.
Ans: a

The speed of the train can be obtained from the time it takes to cross the pole. The speed = \$77/7\$ = 11 m/s. To cross the platform it must travel a total distance equal to the combined lengths of the train and the platform at this speed. So time = \${77 + 616}/11\$ = 63seconds.

### Question 3

A train running at a speed of 14m/s crosses a pole in 18sec. How long will it take to cross a platform of length 1008m?

A

90 sec.

B

91 sec.

C

89 sec.

D

92 sec.

Soln.
Ans: a

The length of the train can be obtained from the time it takes to cross the pole. The length of the train = \$14 × 18\$ = 252m. To cross the platform it must travel a total distance equal to the combined lengths of the train and the platform at this speed. So time = \${252 + 1008}/14\$ = 90 seconds.

### Question 4

Two trains moving in the same direction, and running respectively at 36km/h and 72km/h cross each other in 8sec. What is the length of each train if the two trains are equally long?

A

40 m.

B

41 m.

C

39 m.

D

42 m.

Soln.
Ans: a

The trains cover a distance equal to the sum of their lengths at a relative speed 72 - 36 = 36km/h × (5/18), or 10m/s. We can use the speed distance formula: sum of lengths = 10 × 8 = 80m. Halving this we get the length of one train = 40m.

### Question 5

A train is running at a speed of 182km/h. If it takes 36sec to move past a telegraph pole, then what is its length?

A

1820 meters.

B

1821 meters.

C

1819 meters.

D

1822 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 × (5/18), which gives \$36 × 182 × (5/18)\$ = 1820m. Please note that 5/18 is the conversion from km/h to m/s.