Answer & Solution
Answer: Option B
Solution:
let speed of boat in still water = x km/h
Speed of stream current = y km/h
According to question,
$$\eqalign{
& \frac{{24}}{{x - y}} + \frac{{36}}{{x + y}} = 6h\,......\,(i) \cr
& \frac{{36}}{{x - y}} + \frac{{24}}{{x + y}} = \frac{{13}}{2}h\,......\,(ii) \cr} $$
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)
$$\eqalign{
& \frac{{24}}{{x - y}} + \frac{{36}}{{12}} = 6 \cr
& \frac{{24}}{{x - y}} + 3 = 6 \cr
& x - y = 8 \cr
& \therefore x + y = 12 \cr
& \therefore x = 10\,\,\,,\,\,\,\,y = 2 \cr
& {\text{Speed of the current,}} \cr
& y = 2{\text{ km/h}} \cr} $$