anupamdev wrote:

A train X departs from station A at 11.00 am for station B, which is 180 km away. Another train Y departs from station B at 11.00 am for station A. Train X travels at an average speed of 70 kms/hr and does not stop any where until it arrives at station B. Train Y travels at an average speed of 50 kms/hr, but has to stop for 15 minutes at station C, which is 60 kms away from station B en route to station A. Ignoring the lengths the train, what is the distance, to the nearest km, from station A to the point where the trains cross each other?

A. 112

B. 118

C. 120

D. 122

E. Cant be determined

Train X has a speed of 70 km/hr

Train Y has a speed of 50 Km/hr

Lets solve this problem step by step :

Step 1 : If there is no stoppage at C, time taken by both trains to cross each other = 180/(70+50) = 180/120 = 1.5 hrs

Step 1: Y reaches station C

Time taken by Y = 60/50 = 6/5 hrs. So, till this time trains will not cross each other as 6/5 < 1.5 hrs.

Distance traveled by Y = 60 Km

Distance traveled by X in this time = 70*6/5 = 84 Km

Total distance traveled by both trains = 60+84 = 114 km.

Step 2 : Y is at station C for 15 minutes

Distance traveled by x till this time = 70 (6/5+1/4) = 70 *1.45 = 101.5

Total distance traveled by both trains = 101.5 +60 = 161.5 . So, even after 15 minutes of stoppage of Y, the trains didn't cross each other.

Step 3: Y starts running again after 15 minutes stoppage at station C.

Now, total distance left to travel = 180 - 161.5 = 18.5 km

Time taken by both trains to cover this distance = 18.5/120

Distance traveled by train X in this 28.5 km = 70/120 * 18.5 = 10.791 km

Total distance traveled by train X = 101.5 +10.791 = 112.291 km

So, distance from station A to the point where trains cross each other = 112.291 km ~ 112 km

Answer A
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