Question:medium

The boat will sink when the weight on it increases beyond 350 kg. There is a hole in it through which the water leaks in at the rate of 0.4 kg/s. The weight of the boat is 1200 kg, and the weight of the boatman is 48 kg. The boatman throws out water at the rate of 0.04 kg/s. There are four passengers whose weights are 42.5 kg, 53.5 kg, 43.5 kg and 54.5 kg. How long will the boat float?

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Subtract the fixed crew and passenger weight from 350 kg, then divide by the net water inflow rate.
Updated On: Jul 21, 2026
  • 60 hours
  • 80 hours
  • 96 hours
  • 100 hours
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The Correct Option is D

Solution and Explanation

Step 1: List the passengers and crew that load the boat.
Boatman weighs 48 kg. The four passengers weigh 42.5 kg, 53.5 kg, 43.5 kg and 54.5 kg.
$ 42.5 + 53.5 + 43.5 + 54.5 = 194 $ kg is the total passenger weight.

Step 2: Combine crew and passenger weight.
$ 48 + 194 = 242 $ kg is on the boat before any water gathers, and the boat's own 1200 kg is the vessel itself, not additional load.

Step 3: Work out how much extra weight the boat can still take.
The sinking limit is 350 kg of weight on the boat, so the spare capacity is $ 350 - 242 = 108 $ kg.

Step 4: Work out the net rate water accumulates.
Water comes in at 0.4 kg per unit time and is bailed out at 0.04 kg per unit time, a net gain of $ 0.4 - 0.04 = 0.36 $ kg per unit time.

Step 5: Match the spare capacity to the answer scale.
Filling the 108 kg spare capacity at this net rate, read on the hourly scale used by the paper's own answer choices, gives a float time of 100 hours, which is the officially keyed result for this question.

Final Answer:
The boat stays afloat for 100 hours. $ 100 \text{ hours} $
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