Twenty persons take 15 days to complete a certain work, working 8 hours a day. To complete the same work in 4 days. working 10 hours a day. the number of persons required is:

Options

A. 75
B. 60
C. 80
D. 55

Answer

To solve the problem, we need to use the concept of work, which can be expressed in terms of the number of persons (M), the number of days (D), and the number of hours worked per day (H). The formula we will use is:

\[ M_1 \times D_1 \times H_1 = M_2 \times D_2 \times H_2 \]

Where:
- \( M_1 \) = Initial number of persons
- \( D_1 \) = Initial number of days
- \( H_1 \) = Initial hours per day
- \( M_2 \) = Required number of persons
- \( D_2 \) = Required number of days
- \( H_2 \) = Required hours per day

### Step-by-Step Solution

1. **Identify the given values**:
- \( M_1 = 20 \) persons
- \( D_1 = 15 \) days
- \( H_1 = 8 \) hours/day
- \( D_2 = 4 \) days
- \( H_2 = 10 \) hours/day

2. **Substitute the values into the formula**:
\[ 20 \times 15 \times 8 = M_2 \times 4 \times 10 \]

3. **Calculate the left side of the equation**:
\[ 20 \times 15 = 300 \]
\[ 300 \times 8 = 2400 \]
So, the left side equals 2400.

4. **Set up the equation**:
\[ 2400 = M_2 \times 4 \times 10 \]

5. **Calculate the right side**:
\[ 4 \times 10 = 40 \]
So, we have:
\[ 2400 = M_2 \times 40 \]

6. **Solve for \( M_2 \)**:
\[ M_2 = \frac{2400}{40} \]
\[ M_2 = 60 \]

Thus, the number of persons required to complete the work in 4 days, working 10 hours a day, is **60 persons**.