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Speed of boat in still water is 9 km/hr. Stream speed initially is 2 km/hr but it increases by 3 km/hr after every hour. Find the time after which boat will come back to the position where it started.(in hour)


1. 5(5/8)
2. 4(7/8)
3. 5(3/8)
4. 4(3/4)
5. None of these

1 Answer

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Correct Answer - Option 1 : 5(5/8)

Given:-

Boat speed = 9 km/hr

Formula:-

Speed = Distance/Time

Upstream speed = u - v

Concept:-

Boat will come back only if it is travelling upstream as after some time stream speed will be more than boat speed and boat will start travelling in backwards direction.

Calculation:-

Distance travelled in first hour = (9 - 2) × 1 = 7 km

Distance travelled in second hour = (9 - 2 - 3) × 1 = 4 km

Distance travelled in third hour = (9 - 2 - 3 - 3) × 1 = 1 km

Distance travelled in fourth hour = (1 - 3) × 1 = - 2 km or 2 km in backward direction.

After 4 hours boat is at a distance of (7 + 4 + 1 - 2) = 10 km from starting point.

Distance in fifth hour = (- 2 - 3) × 1 = - 5 km

Now boat will be (10 - 5) = 5 km away

Time for next 5 km = 5/(- 5 - 3) = 5/8 hour (ignore negative sign for time)

So boat will be back in 5(5/8) hours.

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