Question : The speed of a motorboat in still water and the speed of the current of water is in the ratio 20 : 4. To go a certain distance along the current the boat takes 4 hours. Find the time taken by the boat to cover the same distance against the current.
Option 1: 6 hours
Option 2: 8 hours
Option 3: 12 hours
Option 4: 10 hours
Correct Answer: 6 hours
Solution :
Speed of boat along the current = speed of the boat in still water + speed of the current of water
Speed of boat against the current = speed of the boat in still water – speed of the current of water
Let the Speed of the boat in still water be $20x$ then the speed of the water current is $4x$
and the certain distance covered is $d$.
Speed of boat along the stream $= 20x + 4x = 24x$ km/hr
Time taken = 4 hours
Distance = speed × time
⇒ $d = 24x × 4= 96x$ km
So, the distance travelled is $96x$ km.
Speed of the boat against the stream $= 20x - 4x = 16x$ km/hr
Now, Time $= \frac{\text{Distance}}{\text{Speed}}= \frac{96x}{16x} = 6$ hours
Hence, the correct answer is 6 hours.
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