45 people take 18 days to dig a pond. If the pond would have to be dug in 15 days, then the number of people to be employed will be

Options

A. 50
B. 54
C. 60
D. 72

Answer

To solve the problem step by step, we can use the concept of work done, which is based on the formula:

\[ \text{Work} = \text{Number of People} \times \text{Number of Days} \]

Given:
- \( M_1 = 45 \) (initial number of people)
- \( D_1 = 18 \) (initial number of days)
- \( M_2 = ? \) (number of people needed)
- \( D_2 = 15 \) (new number of days)

### Step 1: Calculate the total work done in terms of person-days.
The total work done to dig the pond can be calculated using the initial number of people and the number of days they worked.

\[ \text{Total Work} = M_1 \times D_1 = 45 \times 18 \]

### Step 2: Calculate the total work.
Now, let's calculate the total work:

\[ \text{Total Work} = 45 \times 18 = 810 \text{ person-days} \]

### Step 3: Set up the equation for the new scenario.
In the new scenario, we need to find out how many people are required to complete the same amount of work in 15 days. We can set up the equation as follows:

\[ \text{Total Work} = M_2 \times D_2 \]

Substituting the known values:

\[ 810 = M_2 \times 15 \]

### Step 4: Solve for \( M_2 \).
Now, we can solve for \( M_2 \):

\[ M_2 = \frac{810}{15} \]

### Step 5: Calculate \( M_2 \).
Now, let's calculate \( M_2 \):

\[ M_2 = \frac{810}{15} = 54 \]

### Conclusion:
Therefore, the number of people that need to be employed to dig the pond in 15 days is \( M_2 = 54 \).

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