Twelve persons can do a piece of work in 20 days. How many persons are required to do the same in 24 days?

Options

A. 20
B. 10
C. 15
D. 18

Explanation

To solve the problem step by step, we can use the concept of work done, which is based on the relationship between the number of persons, the number of days, and the total work.

### Step-by-Step Solution:

1. **Understand the Work Done**:
We know that 12 persons can complete a piece of work in 20 days. We can express the total work in terms of person-days.
\[ \text{Total Work} = \text{Number of Persons} \times \text{Number of Days} = 12 \text{ persons} \times 20 \text{ days} = 240 \text{ person-days} \]

2. **Determine the Work Rate**:
The work rate can be understood as how much work one person can do in one day. Since 12 persons complete the work in 20 days, we can find out how many persons are needed to complete the same work in 24 days.

3. **Set Up the Equation**:
Let \( x \) be the number of persons required to complete the same work in 24 days. The total work remains the same (240 person-days):
\[ x \text{ persons} \times 24 \text{ days} = 240 \text{ person-days} \]

4. **Solve for \( x \)**:
To find \( x \), we rearrange the equation:
\[ x = \frac{240 \text{ person-days}}{24 \text{ days}} = 10 \text{ persons} \]

5. **Conclusion**:
Therefore, the number of persons required to do the same work in 24 days is **10 persons**.

### Final Answer:
10 persons are required to do the work in 24 days.

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