| A boat running downstream covers a distance of 30 km in 2 h. While coming back the boat takes 6 h to cover the same distance. If the speed of the current is half that of the boat, what is the speed of that boat? |
| [IBPS (Office Assistant) 2015] |
A) 15 km/h
B) 5 km/h
C) 10 km/h
D) 20 km/h
E) None of these
Correct Answer: B
Solution :
| Speed of boat = x |
| Speed of stream = y |
| Speed downstream \[=x+y\] |
| We know that, \[\text{Speed}=\frac{\text{Distance}}{\text{Time}}\] |
| Boat covers 30 km in 2 h in downstream |
| Speed of boat downstream \[=\frac{30}{2}=15\,km/h\] (i) |
| Speed of current (stream) \[=\frac{1}{2}th\] speed of boat |
| \[y=\frac{1}{2}x\] |
| \[\Rightarrow \] \[x=2y\] (ii) |
| Speed downstream \[=x+y\] |
| \[15=y+2y\] |
| \[\Rightarrow \] \[3y=15\]\[\Rightarrow \]\[y=5km/h\] |
| Speed of stream \[=\,5\,km/h\] |
| Speed of boat \[=10\,km/h\] |
| Speed upstream \[=x-y=10-5=5\,km/h\] |
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