A boat can go 40 km downstream and 25 km upstream in 7 hours 30 minutes. It can go 48 km downstream and 36 km upstream in 10 hours. What is the speed (in km/h) of the boat in still water?

Solution (By Examveda Team)

$$\eqalign{ & {\text{Speed of boat}} = x \cr & {\text{Speed of current}} = y \cr & {\text{According to the question,}} \cr & \frac{{40}}{{x + y}} + \frac{{25}}{{x - y}} = \frac{{15}}{2} \cr & {\text{Multiplying both sides by}}\frac{6}{5}{\text{ and}} \cr & \frac{{40}}{{x + y}} + \frac{{30}}{{x - y}} = \frac{{18}}{2} \cr & \frac{{40}}{{x + y}} + \frac{{30}}{{x - y}} = 9\,.\,.\,.\,.\,.\,.\,.\,\left( 1 \right) \cr & \frac{{48}}{{x + y}} + \frac{{36}}{{x - y}} = 10\,.\,.\,.\,.\,.\,.\,.\,\left( 2 \right) \cr & \underline {\,\, - \,\,\,\,\,\,\,\,\,\, - \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, - \,\,\,\,\,\,\,\,} \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\frac{{ - 6}}{{x - y}} = - 1 \cr & x - y = 6\,.\,.\,.\,.\,.\,.\,.\,\left( 3 \right) \cr & {\text{From equation }}\left( 2 \right), \cr & \frac{{48}}{{x + y}} + \frac{{36}}{6} = 10 \cr & \frac{{48}}{{x + y}} = 4 \cr & x + y = 12\,.\,.\,.\,.\,.\,.\,.\,\left( 4 \right) \cr & {\text{From equation }}\left( 3 \right){\text{ and }}\left( 4 \right) \cr & x - y = 6 \cr & x + y = 12 \cr & \overline {\,x = 9,\,y = 3\,} \cr & {\text{Speed of boat}} = 9 \cr} $$