A boat covers 24 km upstream and 36 km downstream in 6 hours, while it covers 36 km upstream and 24 km downstream in 6¹/₂ hours. The speed of the current is?

Explanation:-

$$\eqalign{ & {\text{let speed of boat in still water}} \cr & {\text{ = }}x{\text{ }}km/h \cr & {\text{Speed of stream current}} \cr & {\text{ = }}y{\text{ }}km/h \cr & {\text{According to question(ATQ)}} \cr & \frac{{24}}{{x - y}} + \frac{{36}}{{x + y}} = 6h\,...........\,(i) \cr & \frac{{36}}{{x - y}} + \frac{{24}}{{x + y}} = \frac{{13}}{2}h\,.............\,(ii) \cr & {\text{In these type of questions, make factor of }} \cr & {\text{24 and 36 and choose the common values}} \cr & {\text{which satisfy the above equations}}{\text{.}} \cr & {\text{24 = 2,3,4,6,8,}}\boxed{12} \cr & 36 = 3,4,9,\boxed{12} \cr & {\text{Choose the common factor i}}{\text{.e}}{\text{. }} \cr & {\text{Put this value in equation (i)}} \cr & \frac{{24}}{{x - y}} + \frac{{36}}{{12}} = 6 \cr & \frac{{24}}{{x - y}} + 3 = 6 \cr & x - y = 8 \cr & \therefore x + y = 12 \cr & \therefore x = 10\,\,\,,\,\,\,\,y = 2 \cr & {\text{Speed of the current,}} \cr & y = 2{\text{ }}km/h \cr}$$