Question : A boat goes 4 km upstream and 4 km downstream in an hour. The same boat goes 5 km downstream and 3 km upstream in 55 minutes. What is the speed (in km/hr) of the boat in still water?
Option 1: 6.5
Option 2: 7.75
Option 3: 9
Option 4: 10.5
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Correct Answer: 9
Solution :
Let the speed of the boat in still water be $a$ km/hr and the speed of water be $b$ km/hr.
Speed in downstream = $a+b$
Speed in upstream = $a-b$
As per the first given condition:
$⇒ \frac{4}{(a-b)}+\frac{4}{(a+b)}=1$
Let $\frac{1}{(a-b)}=x$ and $\frac{1}{(a+b)}=y$
$⇒4x+4y=1$
$⇒ x+y =\frac{1}{4} $ --------------------------(1)
As per the second given condition:
$⇒\frac{3}{(a-b)}+\frac{5}{(a+b)}=\frac{55}{60}$
$⇒3x+5y=\frac{11}{12}$
By putting the value of $y$ from equation (1) we get:
$⇒3x+5(\frac{1}{4}-x)=\frac{11}{12}$
$⇒2x=\frac{5}{4}-\frac{11}{12}$
$⇒x=\frac{1}{6}⇒(a-b)=6$ ----------------------------(2)
By putting the value of $x$ in equation (1)
$⇒y=\frac{1}{4}-\frac{1}{6}$
$⇒y=\frac{1}{12}⇒(a+b)=$ 12 --------------------(3)
From equation (2) and (3),
$⇒2a= 18⇒a= 9$
The speed of the boat in still water is 9 km/hr.
Hence, the correct answer is 9.
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