A boat goes 15 km upstream and 22 km downstream is 5 hours. It goes 20 km upstream and $$\ \frac{55}{2}\ $$km downstream in $$\ \frac{13}{2}\ $$hours. What is the speed (in km/hr) of stream ?

Let speed of boat = $$x$$ km/hr and speed of stream = $$y$$ km/hr

=> Downstream speed = $$(x+y)$$ km/hr and Upstream speed = $$(x-y)$$ km/hr

According to ques,

=> $$\frac{15}{x-y}+\frac{22}{x+y}=5$$

and $$\frac{20}{x-y}+\frac{27.5}{x+y}=6.5$$

Let $$\frac{1}{x-y}=m$$ and $$\frac{1}{x+y}=n$$

=> $$15m+22n=5$$ and $$20m+27.5n=6.5$$

Solving above equations, we get : $$m=\frac{1}{5}$$ and $$n=\frac{1}{11}$$

Thus, $$x-y=5$$ and $$x+y=11$$

Subtracting both equation, => $$2y=11-5=6$$

=> $$y=\frac{6}{2}=3$$

$$\therefore$$ Speed of stream = 3 km/hr

=> Ans - (A)