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A train A leaves Station X at 7 a.m. and reaches Station Y at 11 a.m. Another train B leaves Station Y at 9 a.m. and reaches Station X at 12.30 p.m. The distance between these two stations are 28 km. At what time do the two trains cross each other?

A train A leaves Station X at 7 a.m. and reaches Station Y at 11 a.m. Another train B leaves Station Y at 9 a.m. and reaches Station X at 12.30 p.m. The distance between these two stations are 28 km. At what time do the two trains cross each other? Correct Answer 9.56 a.m.

Distance = 28 km

Time taken by train A = 4 hrs

Speed of train A = 28/4 = 7 km/hr

Time taken by train B = 3.5 hrs

Speed of train B = 28/3.5 = 8 km/hr

When they cross the total distance travelled by both trains = 28 km

Let t = time (hrs) of first train

Then, time of second train = (t - 2) hrs

Distance = speed × time

⇒ 7t + 8(t - 2) = 28

⇒ 7t + 8t - 16 = 28

⇒ 15t = 28 + 16

⇒ t = 44/15 = 2 hrs 56 min travel time of first train when they cross

2 hr 56 min from 7 a.m. = 9:56 a.m.

∴ Time when they cross is 9:56 a.m.

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