If 10 persons can do a job in 24 days, then 20 persons with twice the efficiency can do the same job in :

Options

A. 5 days
B. 10 days
C. 12 days
D. 6 days

Answer

To solve the problem, we need to determine how long it will take for 20 persons with twice the efficiency to complete the same job that 10 persons can do in 24 days.

### Step-by-Step Solution:

1. **Identify the Work Done by 10 Persons**:
- Given that 10 persons can complete the job in 24 days, we can denote the total work as \( W \).
- The work done by 10 persons in 24 days can be represented as:
\[ W = 10 \text{ persons} \times 24 \text{ days} \times 1 \text{ efficiency unit} = 240 \text{ person-days} \]

2. **Determine the Efficiency of 20 Persons**:
- If 20 persons have twice the efficiency, then their effective efficiency can be calculated as:
\[ \text{Efficiency of 20 persons} = 20 \text{ persons} \times 2 \text{ (twice the efficiency)} = 40 \text{ efficiency units} \]

3. **Calculate the Time Taken by 20 Persons**:
- We need to find how many days \( D \) it will take for these 20 persons with 40 efficiency units to complete the same amount of work \( W \):
\[ W = \text{Efficiency} \times \text{Time} \]
- Therefore, we can set up the equation:
\[ 240 \text{ person-days} = 40 \text{ efficiency units} \times D \]
- Rearranging gives:
\[ D = \frac{240 \text{ person-days}}{40 \text{ efficiency units}} = 6 \text{ days} \]

4. **Conclusion**:
- Thus, 20 persons with twice the efficiency can complete the job in **6 days**.

### Final Answer:
The answer is **6 days**.