30 persons can do a piece of work in 24 days. How many more people are required to complete the work in 20 days?

Options

A. 4
B. 5
C. 6
D. none of these

Answer

To solve the problem step by step, we will use the relationship between the number of workers, the number of days, and the amount of work done.

### Step 1: Understand the given data
We know that:
- 30 persons can complete the work in 24 days.

### Step 2: Calculate the total work in terms of person-days
Total work can be calculated as:
\[ \text{Total Work} = \text{Number of Persons} \times \text{Number of Days} \]
So, in this case:
\[ \text{Total Work} = 30 \text{ persons} \times 24 \text{ days} = 720 \text{ person-days} \]

### Step 3: Determine the number of persons required to complete the work in 20 days
Let \( M_2 \) be the number of persons required to complete the same work in 20 days. We can set up the equation:
\[ M_2 \times 20 \text{ days} = 720 \text{ person-days} \]
To find \( M_2 \), we rearrange the equation:
\[ M_2 = \frac{720 \text{ person-days}}{20 \text{ days}} = 36 \text{ persons} \]

### Step 4: Calculate how many more persons are needed
We need to find out how many more persons are required compared to the original 30 persons:
\[ \text{More persons required} = M_2 - M_1 = 36 - 30 = 6 \]

### Final Answer
Thus, the number of additional persons required to complete the work in 20 days is **6 persons**.

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