A boat covers 24 km upstream and 36 km downstream in 6 hours, while it covers 36 km upstream and 24 km downstream in $$6\frac{1}{2}$$ hours. The speed of the current is ?
a) 1 km/hr
b) 2 km/hrs
c) 1.5 km/hrs
d) 2.5 km/hr

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