If 24 men can do a work in 15 days by working 12 hours daily, then in how many days will 36 men be able to do double the quantum of work, by working 10 hours daily?

Options

A. 30
B. 32
C. 24
D. 12

Answer

To solve the problem, we need to follow these steps:

### Step 1: Calculate the total work done by 24 men in 15 days.
The total work can be calculated using the formula:
\[ \text{Total Work} = \text{Number of Men} \times \text{Number of Days} \times \text{Hours per Day} \]

Given:
- Number of Men = 24
- Number of Days = 15
- Hours per Day = 12

So, the total work is:
\[ \text{Total Work} = 24 \times 15 \times 12 \]

Calculating this:
\[ \text{Total Work} = 24 \times 15 = 360 \]
\[ \text{Total Work} = 360 \times 12 = 4320 \text{ man-hours} \]

### Step 2: Determine the total work needed for double the quantum of work.
Since we need double the work:
\[ \text{Double Work} = 2 \times 4320 = 8640 \text{ man-hours} \]

### Step 3: Calculate the daily work done by 36 men working 10 hours daily.
Now, we need to find out how many days it will take for 36 men to do 8640 man-hours of work, working 10 hours a day.

First, calculate the daily work done by 36 men:
\[ \text{Daily Work} = \text{Number of Men} \times \text{Hours per Day} \]
\[ \text{Daily Work} = 36 \times 10 = 360 \text{ man-hours per day} \]

### Step 4: Calculate the number of days required to complete the double work.
Now, we can find the number of days required to complete the double work:
\[ \text{Number of Days} = \frac{\text{Total Work}}{\text{Daily Work}} \]
\[ \text{Number of Days} = \frac{8640}{360} \]

Calculating this:
\[ \text{Number of Days} = 24 \]

### Final Answer:
The number of days required for 36 men to complete double the work by working 10 hours daily is **24 days**.

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