Question

A is thrice as efficient as B. Working together, they complete the work in 3 days. If working alone, B takes 8 days more than A to finish the whole work. What is the number of days taken by A to finish the whole work alone?

• A. \(6\)
• B. \(4\)
• C. \(8\)
• D. \(12\)
• E. \(10\)

Answer 1

The Correct Option is B

Concept: Efficiency ratio: \[ A : B = 3 : 1 \]
Step 1: Let work rates.
\[ A = 3x,\quad B = x \] \[ A+B = 4x = \frac{1}{3} \Rightarrow x = \frac{1}{12} \]
Step 2: Individual times.
\[ A = \frac{1}{3x} = \frac{1}{3 \times \frac{1}{12}} = 4 \text{ days} \] \[ B = \frac{1}{x} = 12 \text{ days} \] Check: \[ B = A + 8 \Rightarrow 12 = 4 + 8 \quad \checkmark \]
Step 3: 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).