question_answer

A swimmer swims from a point A against a current for 5 minutes and then swims backwards in favour of the current for next 5 minutes and comes to the point B. If \[AB=100\]metres, the speed of the current (in km per hour) is :

A)  \[0.4\]             

B)       0.2

C)  1                    

D)       \[0.6\]

Correct Answer: D

Solution :

The distance covered upstream \[=AC=d\] \[AB=100\] \[BC=100+d\] Rate upstream = \[(x-y)\] m/minute Rate downstream =\[(x+y)\] m/minute             \[\therefore \]    \[\frac{d}{x-y}=5\]             \[\Rightarrow \]            \[d=5\,\,(x-y)\]                ?..(i)             Again, \[\frac{100+d}{x+y}=5\]             \[\Rightarrow \]            \[\frac{100+5(x-y)}{x+y}=5\] \[\Rightarrow \]            \[100+5x-5y=5x+5y\] \[\Rightarrow \]            \[10y=100\] \[\Rightarrow \]            \[y=10\,m/\text{minute}\]             \[=\frac{10}{1000}\times 60\,\,kmph\]             \[=0.6\,\,kmph\]