Problems on Trains Quiz Set 001 | Maths Aptitude Quiz Questions and Mock Test on Problems on Trains Set 1 | mock tests for Bank PO, SSC Exams, SO Clerical Exam, GATE Exam, LIC AO, GIC AO, etc.

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Question 1

A train passes two persons walking in the same direction as the train. The time it takes to move past the man running at 32km/h is 10sec, whereas the time it takes to cross the other man running at 34km/h is 11sec. What is the speed of the train?

54 km/h.

55 km/h.

53 km/h.

56 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 = $(v - 32) × 10$. It should equal the length obtained from the data for the second man. So $(v - 32) × 10$ = $(v - 34) × 11$. Please note that we have not converted seconds to hours because that factor will ultimately cancel away. Solving for v we get 54km/h.

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Question 2

Two trains start simultaneously. The first train moves from A to B, whereas the second train moves from B to A. After they meet at a point in between, they respectively take 144 hours and 4 hours to reach their destinations. What is the ratio of their speeds?

${1/6}$.

${7/5}$.

${13/8}$.

${19/8}$.

Soln.
Ans: a

If they take $t_1 and t_2$ hours respectively to reach their destinations, then the ratio of their speeds is $√t_2 : √t_1$. So we get $√4 : √144$, which gives 2 : 12, or ${1/6}$.

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Question 3

A train running at a speed of 19m/s crosses a pole in 18sec. How long will it take to cross a platform of length 684m?

54 sec.

55 sec.

53 sec.

56 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 = $19 × 18$ = 342m. 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 = ${342 + 684}/19$ = 54 seconds.

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Question 4

Two trains are moving in same direction on two parallel tracks. How many seconds will they take to cross each other if the sum of their lengths is 82m, and the difference of their speeds is 41m/s?

2 sec.

3 sec.

5 sec.

4 sec.

Soln.
Ans: a

The total distance is equal to the sum of the lengths of the trains, so s = 82. This distance has to be covered at a net relative speed equal to the difference of the speeds of the two trains, so v = 41. The time will be distance/speed = $82/41$ = 2s.

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Question 5

Two trains are moving in opposite directions on two parallel tracks. How many seconds will they take to cross each other if the sum of their lengths is 357m, and the sum of their speeds is 51m/s.?

7 sec.

8 sec.

6 sec.

9 sec.

Soln.
Ans: a

The total distance is equal to the sum of the lengths of the trains, so s = 357. This distance has to be covered at a net relative speed equal to the sums of the speeds of the two trains, so v = 51. The time will be distance/speed = $357/51$ = 7 sec.

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