A man can row at a speed of $$4\frac{1}{2}$$ km/hr in still water. If he takes 2 times as long to row a distance upstream as to row the same distance downstream, then the speed of stream (in km/hr) is-

Solution (By Examveda Team)

$$\eqalign{ & {\text{Speed of man in still water , }} \cr & x{\text{ }} = {\text{ }}\frac{9}{2}km/hr{\text{ }} \cr & {\text{let speed of stream = }}y{\text{ }}km/h \cr & {\text{Downstream speed = }} {\frac{9}{2} + y} \cr & {\text{Upstream speed = }} {\frac{9}{2} - y} \cr & {\text{Accroding to questions,}} \cr & {\text{2}} \times {\frac{{{\text{Distance}}}}{{ {\frac{9}{2} + y} }}} = \frac{{{\text{Distance}}}}{{ {\frac{9}{2} - y} }} \cr & \Rightarrow \frac{2}{{\frac{9}{2} + y}} = \frac{1}{{\frac{9}{2} - y}} \cr & \Rightarrow \frac{{2 \times 2}}{{9 + 2y}} = \frac{2}{{9 - 2y}} \cr & \Rightarrow \frac{2}{{9 + 2y}} = \frac{1}{{9 - 2y}} \cr & \Rightarrow 18 - 4y = 9 + 2y \cr & \Rightarrow 6y = 9 \cr & \Rightarrow y = \frac{9}{6} = \frac{3}{2} = 1.5\,km/h \cr} $$