Question : The speed of a boat in still water is 20 km/hr, while the river is flowing at a speed of 8 km/hr and the time taken to cover a certain distance upstream is 6 hr more than the time taken to cover the same distance downstream. Find the distance.
Option 1: 120 km
Option 2: 336 km
Option 3: 126 km
Option 4: 125 km
Correct Answer: 126 km
Solution : The speed of a boat in still water = 20 km/hr Speed of river = 8 km/hr Upstream speed = 20 – 8 = 12 km/hr Downstream speed = 20 + 8 = 28 km/hr Let $x$ be the distance. Time taken to cover the distance upstream = $\frac{x}{12}$ hr Time taken to cover the distance downstream = $\frac{x}{28}$ hr Difference = 6 hr So, $\frac{x}{12}-\frac{x}{28}=6$ ⇒ $\frac{7x-3x}{84} = 6$ ⇒ $\frac{4x}{84}=6$ ⇒ $\frac{x}{21}=6$ ⇒ $x = 21 × 6 = 126$ km Hence, the correct answer is 126 km.
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