Question : A boat moves 25 km upstream and 39 km downstream in 8 hours. It travels 35 km upstream and 52 km downstream in 11 hours. What is the speed of the stream if it travels at a uniform speed?
Option 1: 4 km/hr
Option 2: 5 km/hr
Option 3: 6 km/hr
Option 4: 3 km/hr
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Correct Answer: 4 km/hr
Solution :
Let the speed of the boat be $x$ and that of the stream be $y$.
According to the question,
$\frac{25}{x-y}+\frac{39}{x+y}=8$ ----------------- (1)
$\frac{35}{x-y}+\frac{52}{x+y}=11$ ----------------- (2)
Multiplying equation (1) by 4 and equation (2) by 3 and then subtracting equation (2) from (1), we get,
$\frac{105}{x-y}-\frac{100}{x-y}=33-32$
$⇒\frac{5}{x-y}=1$
$⇒x-y=5$ -----------------------------(3)
Now, putting the value of $x-y$ in equation (1), we get,
$5 + \frac{39}{x+y} = 8$
$⇒x+y =13$ --------------------------(4)
Now, Subtracting equation (3) from equation (4),
$x+y-x+y=13-5$
$⇒2y=8$
$\therefore y=4$
So, the speed of the stream is 4 km/hr.
Hence, the correct answer is 4 km/hr.
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