Question : A boat can cover 120 km upstream and back in a total of 30 hours, and 25 km upstream and 40 km downstream in a total of 7 hours. How much distance will the boat cover in 16 hours in still water?
Option 1: 200 km
Option 2: 180 km
Option 3: 175 km
Option 4: 225 km
Correct Answer: 200 km
Solution :
Let the speed of the boat in still water be $x$ km/hr and the speed of the current be $y$ km/hr.
Speed downstream = $x + y$
Speed upstream = $x - y$
Now, $\text{Time} = \frac{\text{Distance}}{\text{Speed}}$
$\frac{120}{x + y} + \frac{120}{x - y} = 30$....(1)
and$\frac{40}{x + y} + \frac{25}{x – y} = 7$ ....(2)
Multiplying equation (2) by 3, we get,
$\frac{120}{x + y} + \frac{75}{x – y} = 21$ ......(3)
Subtracting equation (3) from (1), we get,
$\frac{45}{x – y} = 9$
$⇒x - y = 5$.......(4)
Putting the value of $x - y$ in equation (2), we get,
$x + y = 20$ .......(5)
Solving these two equations, we get the values of $x$ and $y$.
$x = 12.5$ and $y = 7.5$
Distance covered by the boat in 16 hours in still water = 16 × 12.5 = 200 km
Hence, the correct answer is 200 km.
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