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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