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Two trains start at the same time from A and B and proceed toward each other at the sped of 75 km/hr and 50 km/hr respectively. When both meet at a point in between, one train was found to have traveled 175 km more then the other. Find the distance between A and B?

A. 875 km

B. 785 km

C. 758 km

D. 857 km

Answer: Option A

Solution(By Examveda Team)

$$\eqalign{ & {\text{Let the trains meet after t hours}} \cr & {\text{Speed of train A}} \cr & {\text{ = 75 km/hr}} \cr & {\text{Speed of train B}} \cr & {\text{ = 50 km/hr}} \cr & {\text{Distance covered by train A}} \cr & {\text{ = 75}} \times {\text{t = 75t}} \cr & {\text{Distance covered by train B}} \cr & {\text{ = 50}} \times {\text{t = 50t}} \cr & {\text{Distance}}\,{\text{ = Speed }} \times {\text{Time}} \cr & {\text{According to question}} \cr & 75{\text{t}} - 50{\text{t}} = 175 \cr & \Rightarrow 25{\text{t}} = 175 \cr & \Rightarrow {\text{t}} = \frac{{175}}{{25}} = 7\,{\text{hour}} \cr & \therefore {\text{Distance between A and B }} \cr & {\text{ = 75t}} + 50{\text{t}} = 125{\text{t}} \cr & = 125 \times 7 = 875\,{\text{km}} \cr} $$

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