x boys can do a piece of work in 24 days. In how much time (in days), 2x boys will do half of the work?

Options

A. 6
B. 12
C. 18
D. 8

Answer

To solve the problem step by step, we will use the relationship between work, manpower, and time.

### Step-by-Step Solution:

1. **Understand the Work Done by x Boys:**
- Given that x boys can complete a piece of work in 24 days, we can denote the total work as W.
- The work done by x boys in 24 days can be expressed as:
\[ W = x \times 24 \]

2. **Determine the Work Done by 2x Boys:**
- If 2x boys are working, they will have double the manpower compared to x boys.
- Therefore, the work done by 2x boys in one day is:
\[ \text{Work done in 1 day} = 2x \]

3. **Calculate the Time Taken by 2x Boys to Complete the Full Work:**
- The time taken (D) by 2x boys to complete the entire work W can be calculated using the formula:
\[ W = \text{Manpower} \times \text{Days} \]
- Rearranging gives:
\[ D = \frac{W}{\text{Manpower}} = \frac{x \times 24}{2x} = \frac{24}{2} = 12 \text{ days} \]
- Thus, 2x boys can complete the entire work in 12 days.

4. **Calculate the Time Taken to Complete Half of the Work:**
- Since we need to find out how long it takes for 2x boys to complete half of the work, we take half of the total time:
\[ \text{Time for half of the work} = \frac{12}{2} = 6 \text{ days} \]

### Final Answer:
2x boys will take **6 days** to complete half of the work.

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