A and B cycle from Mumbai to Pune, a distance of 192 kms at 18 km/hr and 14 km/hr respectively. A reaches Pune and starts back for Mumbai. How far from Pune will he meet B?
- 12 kms
- 16 kms
- 24 kms
- 42 kms
- 60 kms
The Usual Method
As can be seen from the figure above that A will have to travel a distance of (192 + x) kms and B travels a distance of (192 – x) kms, so that they both meet at point M.
Thus time taken by A to travel =
And time taken by B to travel =
Since, both A and B start together, time taken by both to meet will be equal.
Estimated Time to arrive at the answer = 90 seconds.
Distance traveled by A and B will be in the ratio of their speeds since time taken to meet is same for both. Thus ratio of distance traveled by A and B = ratio of speeds of A and B = 18 : 14 = 9 : 7.
Total distance traveled by both A and B together = twice the distance between Mumbai and Pune = 2 x 192 = 384 kms. Dividing 384 kms between A and B in the ratio of 9 : 7, we get distance traveled by A = 216 kms.
Hence the meeting point is 192 – 216 = 24 kms from Pune.
Estimated Time to arrive at the answer = 15 seconds.