A is twice as good a workman as B and together they complete a work in 26 days. In how much time will A alone complete the same work?

Question

Accepted Answer

To determine why Option 4 (39 days) is the correct answer, let's analyze the problem step by step.

### Explanation:

1. **Understanding the Problem:**
   - A is twice as good a workman as B. This means A can do twice the amount of work in the same time as B.
   - Together, A and B complete the work in 26 days.

2. **Setting Up the Equations:**
   - Let the amount of work be denoted by W.
   - Let the work done by B in one day be x units. Therefore, the work done by A in one day will be 2x units (since A is twice as efficient as B).
   - Together, A and B complete the work in 26 days, so:
     $$
     (2x + x) \times 26 = W
     $$
     $$
     3x \times 26 = W
     $$
     $$
     W = 78x
     $$

3. **Calculating A's Time to Complete the Work Alone:**
   - A alone does 2x units of work per day.
   - To complete the entire work W, A would take:
     $$
     \frac{W}{2x} = \frac{78x}{2x} = 39 \text{ days}
     $$

4. **Conclusion:**
   - Therefore, A alone will complete the work in 39 days, which corresponds to Option 4.

### Why Other Options are Incorrect:

- **Option 1 (33 days):** 
  - If A could complete the work in 33 days, then the total work W would be $33 \times 2x = 66x$, which contradicts the calculated total work of 78x.

- **Option 2 (35 days):**
  - If A could complete the work in 35 days, then the total work W would be $35 \times 2x = 70x$, which again contradicts the calculated total work of 78x.

- **Option 3 (37 days):**
  - If A could complete the work in 37 days, then the total work W would be $37 \times 2x = 74x$, which does not match the calculated total work of 78x.

By following the logical steps and calculations, we confirm that Option 4 (39 days) is indeed the correct answer, as it aligns with the given conditions and calculations.