24 men working 8 hours a day can finish a work in 10 days. Working at the rate of 10 hours a day, the number of men required to finish the same work in 6 days is:

Options

A. a. 30
B. b. 32
C. c. 34
D. d. 36

Answer

To solve the problem, we will first calculate the total amount of work done in the first scenario and then determine how many men are needed in the second scenario to complete the same work in a different timeframe.

### Step 1: Calculate the total work done in the first scenario.

The total work can be calculated using the formula:
\[ \text{Total Work} = \text{Number of Men} \times \text{Hours per Day} \times \text{Days} \]

From the problem:
- Number of Men = 24
- Hours per Day = 8
- Days = 10

Now, substituting the values into the formula:
\[ \text{Total Work} = 24 \times 8 \times 10 \]

Calculating this:
\[ \text{Total Work} = 1920 \text{ man-hours} \]

### Step 2: Set up the equation for the second scenario.

In the second scenario, we need to find out how many men (let's call this \( x \)) are required to complete the same amount of work (1920 man-hours) when they work:
- Hours per Day = 10
- Days = 6

Using the same formula for total work, we have:
\[ \text{Total Work} = x \times 10 \times 6 \]

### Step 3: Equate the total work from both scenarios.

Since both scenarios complete the same amount of work:
\[ 1920 = x \times 10 \times 6 \]

### Step 4: Solve for \( x \).

First, calculate \( 10 \times 6 \):
\[ 10 \times 6 = 60 \]

Now, we can rewrite the equation:
\[ 1920 = x \times 60 \]

To find \( x \), divide both sides by 60:
\[ x = \frac{1920}{60} \]

Calculating this gives:
\[ x = 32 \]

### Conclusion:

The number of men required to finish the same work in 6 days, working 10 hours a day, is **32 men**.

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