If 28 men complete `(7)/(8)` of a plece of work in a week, then the number of men, who must be engaged to get the remaining work completed in another week, is

Options

A. 5
B. 6
C. 4
D. 3

Answer

To solve the problem step by step, let's break it down:

### Step 1: Determine the amount of work done by 28 men in a week.
Given that 28 men complete \( \frac{7}{8} \) of the work in one week, we can calculate how much work one man can do in a week.

**Calculation:**
- Work done by 28 men in a week = \( \frac{7}{8} \)
- Work done by 1 man in a week = \( \frac{7}{8} \div 28 = \frac{7}{8} \times \frac{1}{28} = \frac{7}{224} = \frac{1}{32} \)

### Step 2: Calculate the remaining work.
The total work is considered as 1 (or 100%). Since \( \frac{7}{8} \) of the work is done, the remaining work is:

**Calculation:**
- Remaining work = Total work - Work done = \( 1 - \frac{7}{8} = \frac{1}{8} \)

### Step 3: Determine how many men are needed to complete the remaining work in one week.
Now we know that one man can complete \( \frac{1}{32} \) of the work in a week. We need to find out how many men are required to complete \( \frac{1}{8} \) of the work in one week.

**Calculation:**
- Let \( x \) be the number of men needed.
- Work done by \( x \) men in one week = \( x \times \frac{1}{32} \)
- We want this to equal \( \frac{1}{8} \):

\[ x \times \frac{1}{32} = \frac{1}{8} \]

### Step 4: Solve for \( x \).
To find \( x \), we can rearrange the equation:

**Calculation:**
\[ x = \frac{1}{8} \div \frac{1}{32} = \frac{1}{8} \times \frac{32}{1} = \frac{32}{8} = 4 \]

### Conclusion:
Thus, the number of men required to complete the remaining work in one week is **4**.

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