Question

Two trains start at the same time from A and B and proceed towards B and A at 36 km/h and 42 km/h, respectively. When they meet, it is found that one train has moved 48 km more than the other. Then, the distance between A and B (in km) is:

• A. 624
• B. 636
• C. 544
• D. 460

Answer 1

The correct option is A 624

Let the two trains be P and Q,
Then, speed ratio = P : Q = 36 : 42 = 6x : 7x
Then ratio of distance covered before the meet = 6x : 7x
and difference of distance covered = 7x - 6x = x = 48.
So, distance between A and B = 7x + 6x = 13x = $13\times 48=624km.$

Alternate Approach:
Let the distance between A and B be x km.
Speed of two trains are 36 km/h and 42 km/h.
Relative speed = 78 km/h
Time taken = $\frac{x}{78}h$
Now, first train has travelled $\frac{x}{78}\times 36=\frac{36x}{78}km$
Second train has travelled $\frac{42x}{78}km.$
Hence, $\frac{42x}{78}-\frac{36x}{78}=48$
or $\frac{6x}{78}=48$
Hence, $x=78\times 8=624km$