Question : A boat can go 40 km downstream and 25 km upstream in 7 hours 30 minutes. It can go 48 km downstream and 36 km upstream in 10 hours. What is the speed (in km/hr) of the boat in still water?
Option 1: 6
Option 2: 12
Option 3: 9
Option 4: 15
Correct Answer: 9
Solution :
Let the speed of a boat in still water be $x$ km/hr and the speed of current water be $y$ km/hr.
Speed in downstream = $x+y$
Speed in upstream = $x-y$
Now, $\frac{40}{x+y}$ + $\frac{25}{x-y}$ = 7.5 ----------(i)
⇒ $\frac{240}{x+y}$ + $\frac{150}{x-y}$ = 45 ----------(ii)
Also $\frac{48}{x+y}$ + $\frac{36}{x-y}$ = 10 ----------(iii)
⇒ $\frac{240}{x+y}$ + $\frac{180}{x-y}$ = 50 ----------(iv)
Equation (iv) – (ii),
⇒ $\frac{30}{(x-y)}$ = 5
⇒ $x-y$ = 6 ---------(v)
From equation (iii) and (v),
⇒ $\frac{48}{x+y}$ + $\frac{36}{6}$ = 10
⇒ $\frac{48}{x+y}$ = 4
⇒ $x+y$ = 12 ---------(vi)
Solving equation (v) & (vi), we get,
⇒ $2x$ = 18
$\therefore x$ = 9 km/hr
Hence, the correct answer is 9.
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