Train A traveling at 60 km hr leaves Mumbai for Delhi at 6 P M Train B traveling at 90 km hr also le...........

Quantitative Aptitude ( CCS) Problems on trains

Train A traveling at 60 km/hr leaves Mumbai for Delhi at 6 P.M. Train B traveling at 90 km/hr also leaves Mumbai for Delhi at 9 P.M. Train C leaves Delhi for Mumbai at 9 P.M. If all three trains meet at the same time between Mumbai and Delhi, what is the speed of Train C if the distance between Delhi and Mumbai is 1260 kms?

150 km

120 km

200 km

Can not say

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Explanation:

All three trains meet at the same time between Delhi and Mumbai. Which means Train A and
Train B are at the same point at that time. This will happen when Train B is overtaking Train A.

Train A starts 3 hours before Train B. Therefore, by the time Train B leaves Mumbai, Train A has
covered 3 * 60 = 180 kms.

The relative speed between Train A and Train B = 90 - 60 = 30 kmph.

Therefore, Train B will overtake Train A in 180/30 = 6 hours from the time Train B leaves Mumbai.

That is at 3 A.M, Train B will overtake Train A.

The point between Mumbai and Delhi at which Train B overtakes Train A will be 6*90=540 kms from Mumbai.
Train C will also be at that point at 3 A.M while Train B is overtaking Train A. And Train C would have travelled 1260-540 = 720 kms in these 6 hours.

Therefore, the speed of Train C = 720/6 = 120 km/hr.

Hence, option 2 is the correct answer.