7 men can complete a plece of work in 12 days. How many additional men will be required to complete double the work in 8 days ?

Options

A. 28
B. 21
C. 14
D. 7

Answer

To solve the problem step by step, we will first determine the total work done and then find out how many additional men are required to complete double the work in the specified time.

### Step 1: Calculate the total work done by 7 men in 12 days.

Let’s denote the total work done by 7 men in 12 days as 1 unit of work.

- Work done by 1 man in 1 day = 1 / (7 men * 12 days) = 1 / 84 units of work.

### Step 2: Calculate the total work for double the work.

Since we need to complete double the work, the total work required will be:

- Total work = 2 units.

### Step 3: Determine the required work rate to finish in 8 days.

To find out how many men are needed to complete 2 units of work in 8 days, we can use the formula:

\[ \text{Work Rate} = \frac{\text{Total Work}}{\text{Days}} = \frac{2 \text{ units}}{8 \text{ days}} = \frac{1}{4} \text{ units per day}. \]

### Step 4: Calculate the number of men required to achieve the work rate.

We know that 1 man can do \(\frac{1}{84}\) units of work in a day. Therefore, to find the number of men (M) required to achieve a work rate of \(\frac{1}{4}\) units per day, we set up the equation:

\[ M \cdot \frac{1}{84} = \frac{1}{4}. \]

### Step 5: Solve for M.

Multiplying both sides by 84 gives us:

\[ M = 84 \cdot \frac{1}{4} = 21 \text{ men}. \]

### Step 6: Calculate the additional men required.

We initially have 7 men. Therefore, the additional men required (x) will be:

\[ x = M - 7 = 21 - 7 = 14. \]

### Final Answer:

**14 additional men will be required to complete double the work in 8 days.**

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