Question : A boat travels 60 kilometres downstream and 20 kilometres upstream in 4 hours. The same boat travels 40 kilometres downstream and 40 kilometres upstream in 6 hours. What is the speed (in km/hr) of the stream?
Option 1: 24 km/hr
Option 2: 16 km/hr
Option 3: 18 km/hr
Option 4: 20 km/hr
Correct Answer: 16 km/hr
Solution :
Time taken to travel 60 km downstream and 20 km upstream = 4 hours
Time taken to travel 40 km downstream and 40 km upstream = 6 hours
Let the speed of the boat in still water be $x$ km/hr and the speed of the current be $y$ km/hr.
According to the question,
$\frac{60}{(x + y)} + \frac{20}{(x − y)} = 4$---------$(i)$
$\frac{40}{(x + y)} + \frac{40}{(x - y)} = 6$----------$(ii)$
Multiply equation (i) by 2 and then subtract equation (ii).
$⇒\frac{80}{(x + y)} = 2$
$⇒x + y = 40$------------------$(iii)$
Putting $x + y = 40$ in equation (i), we get,
$⇒x- y = 8$--------------------------$(iv)$
$\therefore$ On solving $(iii) $and $(iv)$, we get:
Speed of the stream, $y$ = 16 km/hr
Hence, the correct answer is 16 km/hr.
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