Tom Jerry and Bill start from point A at the same time in their cars to go to B Tom reaches point B ...........

Quant (SSC) Time & distance

Tom, Jerry and Bill start from point A at the same time in their cars to go to B. Tom reaches point B first and turns back and meets Jerry at a distance of 9 miles from B. When Jerry reaches B, he too turns back and meets Bill at a distance of 7 miles from B. If 3 times the speed with which Tom drives his car is equal to 5 times Bill’s speed, what could be the distance between the points A and B?

40 miles

24 miles

31 miles

63 miles

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Explanation:

Let the distance between A and B be ‘x’ miles.
Let their speeds be T, J and B in miles/hour
When Tom meets Jerry:
Distance travelled by Tom = x + 9
Distance travelled by Jerry = x – 9
Time taken will be the same => x + 9 /T = x + 9 /J
or T/J = x + 9 /x - 9 ...........(i)
When Jerry meets Bill:
Distance travelled by Jerry = x + 7
Distance travelled by Bill = x – 7
Time taken will be the same => x + 7 /J = x - 7 /B

5(x - 9)(x - 7) = 3 (x + 9)(x + 7)
5x² – 80x + 315 = 3x² + 48x + 189
2x² – 128x + 126 = 0
x² – 64x + 63 = 0
x = 63 or x = 1
Therefore, X has to be 63 miles