Twelve men, working at `8 h` a day, can do a piece of work in `18` days. In how many days can `24` men working at `6 h` a day can do the same work?

Options

A. `12`
B. `16`
C. `20`
D. `30`

Answer

To solve the problem step by step, we will use the concept of work done, which can be expressed as:

\[ \text{Work} = \text{Number of Men} \times \text{Hours per Day} \times \text{Number of Days} \]

### Step 1: Calculate the total work done by the first group of men.

Given:
- Number of men (M1) = 12
- Hours per day (T1) = 8
- Number of days (D1) = 18

Using the formula for work:

\[ \text{Total Work} = M1 \times T1 \times D1 \]

Substituting the values:

\[ \text{Total Work} = 12 \times 8 \times 18 \]

### Step 2: Calculate the total work.

Calculating the above expression:

\[ 12 \times 8 = 96 \]
\[ 96 \times 18 = 1728 \]

So, the total work is 1728 man-hours.

### Step 3: Set up the equation for the second group of men.

Now, we need to find out how many days (D2) it will take for the second group of men to complete the same work.

Given:
- Number of men (M2) = 24
- Hours per day (T2) = 6
- Number of days (D2) = x (unknown)

Using the same work formula:

\[ \text{Total Work} = M2 \times T2 \times D2 \]

Substituting the known values:

\[ 1728 = 24 \times 6 \times x \]

### Step 4: Solve for x (the number of days).

First, calculate \(24 \times 6\):

\[ 24 \times 6 = 144 \]

Now, substituting this back into the equation:

\[ 1728 = 144 \times x \]

To find x, divide both sides by 144:

\[ x = \frac{1728}{144} \]

### Step 5: Calculate the value of x.

Calculating the division:

\[ x = 12 \]

### Conclusion:

Thus, it will take 12 days for 24 men working at 6 hours a day to complete the same work.

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