| The speed of the boat in still water is 24 km/h and the speed of the stream is 4 km/h. The time taken by the boat to travel from A to B downstream is 36 min less than the time taken by the same boat to travel from B to C upstream. If the distance between A and B is 4 km more than the distance between B and C, what is the distance between A and B? |
A) 112 km
B) 140 km
C) 56 km
D) 84 km
E) 28 km
Correct Answer: C
Solution :
| Speed of boat in still water = 24 km/h |
| Speed of stream = 4 km/h |
| Speed of boat in downstream = 28 km/h |
| Speed of boat in upstream = 20 km/h |
| Again, let the distance between B and C = x km |
| Then, distance between A and B \[=(x+4)\,km\] |
| Now, |
| \[\frac{x}{20}-\frac{(x+4)}{28}=\frac{36}{60}\] [difference in time] |
| \[\Rightarrow \] \[\frac{7x-5\,(x+4)}{140}=\frac{3}{5}\] |
| \[\Rightarrow \] \[2x-20=84\] |
| \[\Rightarrow \] \[2x=84+20\] |
| \[\Rightarrow \] \[x=\frac{104}{2}=52\,\,km\] |
| \[\therefore \] Required distance \[=52+4=56\,km\] |
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