A boat goes 8 km upstream and 12 km downstream in 7hours. It goes 9 km upstream and 18 km downstream in 9 hours. What is the speed (in km/h) 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,

=> $$\frac{12}{x+y}+\frac{8}{x-y}=7$$ ----------------(i)

and $$\frac{18}{x+y}+\frac{9}{x-y}=9$$ ----------------(ii)

Applying the operation : $$3\times(i)-2\times(ii)$$

=> $$\frac{24}{x-y}-\frac{18}{x-y}=21-18$$

=> $$\frac{6}{x-y}=3$$

=> $$x-y=\frac{6}{3}=2$$ --------------(iii)

Substituting it in equation (i), => $$\frac{12}{x+y}+\frac{8}{2}=7$$

=> $$\frac{12}{x+y}=7-4=3$$

=> $$x+y=\frac{12}{3}=4$$ ------------(iv)

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

=> $$2x=2+4=6$$

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

=> Ans - (D)