Question 73

A leak was found in a ship when it was 77 km from the shore. It was found that the leak admits 2.25 tonnes of water in 5.5 minutes. 92 tonnes will suffice to sink the ship. But the pumps can throw out the water @ 12 tonnes an hour. Find the average rate of sailing at which the ship may reach the shore as it begins to sink.

Solution

Rate of leak = $$2.25\times\frac{60}{5.5}=\frac{270}{11}$$ tonnes/hr and rate of pump = $$12$$ tonnes/hr

To suffice 92 tonnes, time taken by ship = $$92\div(\frac{270}{11}-12)$$

= $$92\times\frac{11}{138}=\frac{22}{3}$$ hr

=> Average rate of sailing = distance/time

= $$77\div\frac{22}{3}$$

= $$77\times\frac{3}{22}=10.5$$ km/hr

=> Ans - (D)

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