Question

A, B and C are three taps connected to a tank. A and B together can fill the tank in 6 h, B and C together can fill it in 10 h and A and C together can fill it in \(7\frac{1}{2}\) h. In how much time would all three take to fill the tank?

• A. \(6\) h
• B. \(5\) h
• C. \(10\) h
• D. \(12\) h
• E. \(8\) h

Answer 1

The Correct Option is B

Concept: \[ (A+B+C) = \frac{(A+B) + (B+C) + (A+C)}{2} \]
Step 1: Convert into rates.
\[ A+B = \frac{1}{6}, \quad B+C = \frac{1}{10}, \quad A+C = \frac{1}{7.5} = \frac{2}{15} \]
Step 2: Apply formula.
\[ A+B+C = \frac{\frac{1}{6} + \frac{1}{10} + \frac{2}{15}}{2} \] LCM = 30: \[ = \frac{\frac{5 + 3 + 4}{30}}{2} = \frac{12}{30 \times 2} = \frac{12}{60} = \frac{1}{5} \]
Step 3: Time required.
\[ = 5 \text{ hours} \]
Step 4: Option analysis.

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

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