Question

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 she begins to sink.

• A. 9.75 km/h
• B. 13 km/h
• C. 14.5 km/h
• D. 10.5 km/h

Answer 1

The Correct Option is D

Leakage rate= \(2.25\times\frac{60}{5.5}=\frac{135}{5.5}=\frac{270}{11}\) tonnes/hr and pumping rate= 12 tonnes/hr
Time taken by the ship to accommodate 92 tonnes= \(\frac{92}{\frac{270}{11}-12}\)
⇒\(92\times\frac{11}{138}=\frac{22}{3}\space hr.\)
⇒Average rate of sailing = \(\frac{distance}{time}\)
⇒\(\frac{77}{\frac{22}{3}}\)\(=\frac{77\times3}{22}\)\(=10.5 \space km/hr\)
The correct option is (D): 10.5 km/h