How many men need to be emloyed to complete a job in 5 days, if 15 men can complete `(1)/(3)` of the job in 7 days?

Options

A. 20
B. 21
C. 45
D. 63

Answer

To solve the problem, we will follow these steps:

### Step 1: Determine the total work in terms of man-days.
Given that 15 men can complete \( \frac{1}{3} \) of the job in 7 days, we can calculate the total work in man-days.

\[ \text{Work done by 15 men in 7 days} = 15 \text{ men} \times 7 \text{ days} = 105 \text{ man-days} \]

Since this amount of work corresponds to \( \frac{1}{3} \) of the total job, we can find the total work (W) as follows:

\[ W = 105 \text{ man-days} \times 3 = 315 \text{ man-days} \]

### Step 2: Calculate the number of men needed to complete the job in 5 days.
Now, we need to find out how many men (M) are required to complete the total work (315 man-days) in 5 days.

Using the formula for work:

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

We can rearrange this to find the number of men:

\[ M = \frac{W}{D} \]

Substituting the values we have:

\[ M = \frac{315 \text{ man-days}}{5 \text{ days}} = 63 \text{ men} \]

### Final Answer:
Therefore, **63 men** are needed to complete the job in 5 days.

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