A motor boat can travel 40 km downstream and 30 km upstream in 10 hours. It can travel 80 km downstream and 40 km upstream in 15 hours. Find the speed of the boat in still water.

Solution (By Examveda Team)

$$\eqalign{ & {\text{Motor boat}} \cr & \frac{{40}}{{x + y}} + \frac{{30}}{{x - y}} = 10\,.\,.\,.\,.\,.\,\left( 1 \right) \cr & \frac{{80}}{{x + y}} + \frac{{40}}{{x - y}} = 15\,.\,.\,.\,.\,.\,\left( 2 \right) \cr & \frac{{20}}{{x - y}} = 5 \cr & x - y = 4\,.\,.\,.\,.\,.\,\left( 3 \right) \cr & {\text{From equation }}\left( 2 \right),\,\frac{{80}}{{x + y}} + 10 = 15 \cr & x + y = 16\,.\,.\,.\,.\,.\,\left( 4 \right) \cr & {\text{From equation }}\left( 3 \right)\,{\text{and }}\left( 4 \right) \cr & x = 10,\,y = 6 \cr & {\text{Speed of motor boat}} = 10\,{\text{Answer}} \cr & \cr & {\bf{Alternate\, Solution}} \cr & \left( {40 + 30} \right) - \left( {80 + 40} \right) = \left( {10 - 15} \right){\text{hr}} \cr & 5\,{\text{hr}} \to {\text{50 km}} \cr & 1\,{\text{hr}} \to 1{\text{0 km}} \cr & {\text{Speed }} = 1{\text{0 km/hr}} \cr} $$