Question

A ship 156 km from the shore springs a leak which admits \(2\frac{1}{3}\) metric tons of water in \(6\frac{1}{2}\) minutes. A quantity of 68 metric tons would suffice to sink it, but its pumps can throw out 15 metric tons in an hour. The average rate of sailing so that it just reaches the shore as it begins to sink should be

• A. \(16\) km/hr
• B. \(18\) km/hr
• C. \(15\) km/hr
• D. \(14\) km/hr
• E. \(17\) km/hr

Answer 1

The Correct Option is C

Concept: Net filling rate = Inflow $-$ Outflow
Step 1: Convert inflow rate.
\[ 2\frac{1}{3} = \frac{7}{3}, \quad 6\frac{1}{2} = \frac{13}{2} \] \[ \text{Inflow per minute} = \frac{7/3}{13/2} = \frac{14}{39} \] \[ \text{Inflow per hour} = \frac{14}{39} \times 60 = \frac{840}{39} \approx 21.54 \]
Step 2: Net rate.
\[ \text{Net} = 21.54 - 15 = 6.54 \text{ tons/hr} \]
Step 3: Time to sink.
\[ \frac{68}{6.54} \approx 10.4 \text{ hours} \]
Step 4: Speed.
\[ \text{Speed} = \frac{156}{10.4} = 15 \text{ km/hr} \]
Step 5: Option analysis.

• (A) Incorrect $\times$
• (B) Incorrect $\times$
• (C) Correct \checkmark
• (D) Incorrect $\times$
• (E) Incorrect $\times$

Conclusion:
Thus, the correct answer is
Option (C).