A boat covers a distance of 14 km upstream and 16 km downstream in 9 hours. It covers a distance of 12 km upstream and 40 km downstream in 11 hours. What is the speed (in km/hr) of the boat in still water?

Let speed of boat in still water = $$x$$ km/hr and speed of current = $$y$$ km/hr

According to ques,

=> $$\frac{16}{x+y}+\frac{14}{x-y}=9$$ ----------------(i)

and $$\frac{40}{x+y}+\frac{12}{x-y}=11$$ ----------------(ii)

Applying the operation : $$5\times(i)-2\times(ii)$$

=> $$\frac{70}{x-y}-\frac{24}{x-y}=45-22$$

=> $$\frac{46}{x-y}=23$$

=> $$x-y=\frac{46}{3}=2$$ --------------(iii)

Substituting it in equation (i), => $$\frac{16}{x+y}+\frac{14}{2}=9$$

=> $$\frac{16}{x+y}=9-7=2$$

=> $$x+y=\frac{16}{2}=8$$ ------------(iv)

Now, adding equations (iii) and (iv), we get :

=> $$2x=2+8=10$$

=> $$x=\frac{10}{2}=5$$

=> Ans - (A)