# 1000+ Train Problems Aptitude with Answers - 1

Question: 1

Two trains of equal lengths take 10 seconds and 15 seconds respectively to cross a telegraph post. If the length of each train be 120 metres, in what time will they cross each other travelling in opposite direction?

(A) 10 sec

(B) 11 sec

(C) 12 sec

(D) 16 sec

Ans: C

Speed of first train = \$\${120} / {10}\$\$ = 12 m/s

Speed of second train = \$\${120} / {15}\$\$ = 8 m/s

Let t sec be the time in which they cross each other

∴ t = \$\${Total length of trains} /{Relative speed of trains }\$\$ = \$\${120 + 120} / {(12 + 8)}\$\$ = \$\${240} / {20}\$\$ = 12 sec.

Question: 2

Two trains 100 metres and 120 metres long are running in the same direction with speeds of 72 km/hr and 54 km/hr. In how much time will the faster train cross the second?

(A) 40 sec

(B) 42 sec

(C) 44 sec

(D) 46 sec

Ans: C

Relative speed of faster train w.r.t slower train

= 72 - 54 = 18 km/hr = \$\$18 × {5}/ {18}\$\$m/s = 5 m/s

Time taken by the faster train to cross the slower train

= \$\${100 + 120} /{5}\$\$ = 44 sec.

Question: 3

How many seconds will a train 100 metres long running at the rate of 36 km an hour to pass a telegraph post?

(A) 10 seconds

(B) 11 seconds

(C) 12 seconds

(D) 13 seconds

Ans: A

To pass the telegraph post, the train should cover its own length.

∴ Speed of train = 36 km/h = \$\$36 × {5}/{18}\$\$ = 10 m/s.

Required time = \$\${Length of train} / {Speed}\$\$ = \$\${100} / {10}\$\$ = 10 seconds.

Question: 4

Two trains are moving in the same direction at 50 km/h and 30 km/h. The faster train crosses a man in the slower train in 18 seconds. Find the length of the faster train.

(A) 20 m

(B) 50 m

(C) 100 m

(D) 120 m

Ans: C

Relative speed = (50 - 30) km/h = \$\$20 × {5}/{18}\$\$ = \$\${50}/{9}\$\$ m/s

Distance covered in 18 seconds at this speed = \$\${50}/{9} × 18\$\$ = 100 m

∴ Length of faster train = 100 m.

Question: 5

A train is moving at a speed of 120 km/hr. If the length of train is 120 m, how long will it take to cross a railway platform 130 metres long?

(A) 7 sec

(B) 8 sec

(C) \$\$7{1}/{2}\$\$ sec

(D) \$\$8{1}/{2}\$\$ sec

Ans: C

Speed of train = 120 km/hr = \$\$120 × {5}/{18} \$\$ = \$\${100} / {3}\$\$m/s

Time taken by train to cross a platform

= \$\${Length of train + Length of platform} / {Speed of train}\$\$

= \$\${120 + 130} / {100 / 3}\$\$ = \$\${250 × 3} / {100}\$\$ = \$\$7{1}/{2}\$\$sec.

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