12 men can complete a work in 30 days by working 9 hours a day. What is the number of men required to complete 10 times of this work in 24 days by working 5 hours a day ?

Answer

To solve the problem, we will follow these steps:

### Step 1: Calculate the total work done by 12 men in 30 days working 9 hours a day.

Total work (in man-hours) = Number of men × Number of days × Number of hours per day

Total work = 12 men × 30 days × 9 hours/day
Total work = 12 × 30 × 9 = 3240 man-hours

### Step 2: Determine the total work required for 10 times this work.

Since we need to complete 10 times the original work:

Total work required = 10 × 3240 man-hours
Total work required = 32400 man-hours

### Step 3: Calculate the total available work hours with the new conditions.

Now, we need to find out how many men are required to complete this work in 24 days working 5 hours a day.

Total available work hours = Number of men × Number of days × Number of hours per day
Let the number of men required be \( N \).

Total available work hours = \( N \) men × 24 days × 5 hours/day
Total available work hours = \( N \times 24 \times 5 = 120N \) man-hours

### Step 4: Set up the equation.

We know that the total available work hours must equal the total work required:

120N = 32400

### Step 5: Solve for \( N \).

To find \( N \), divide both sides of the equation by 120:

N = 32400 / 120
N = 270

### Conclusion:

The number of men required to complete 10 times the work in 24 days by working 5 hours a day is **270 men**.

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