Fifteen men can complete a piece of work in 10 days, working 8 hours per day. How many persons are required to complete double the work in 25 days, working 6 hours per day ?

Answer

To solve the problem step by step, we can use the concept of work done, which is calculated as the product of the number of men, the number of days, and the number of hours worked per day.

### Step 1: Calculate the total work done by 15 men in 10 days working 8 hours per day.

Total work (W1) = Number of men (M1) × Number of days (D1) × Hours per day (T1)

Given:
- M1 = 15 men
- D1 = 10 days
- T1 = 8 hours/day

\[ W1 = 15 \times 10 \times 8 = 1200 \text{ man-hours} \]

### Step 2: Determine the total work required for double the work.

Since we need to complete double the work, we have:

\[ W2 = 2 \times W1 = 2 \times 1200 = 2400 \text{ man-hours} \]

### Step 3: Set up the equation for the new scenario.

We need to find out how many men (M2) are required to complete this work in 25 days working 6 hours per day.

Total work (W2) can also be expressed as:

\[ W2 = M2 \times D2 \times T2 \]

Where:
- D2 = 25 days
- T2 = 6 hours/day

### Step 4: Substitute the values into the equation.

\[ 2400 = M2 \times 25 \times 6 \]

### Step 5: Solve for M2.

First, calculate \(25 \times 6\):

\[ 25 \times 6 = 150 \]

Now, substitute this back into the equation:

\[ 2400 = M2 \times 150 \]

To find M2, divide both sides by 150:

\[ M2 = \frac{2400}{150} = 16 \]

### Conclusion:

Therefore, **16 men** are required to complete double the work in 25 days working 6 hours per day.

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