Five women can do a work in thirty six days. If the ratio between the capacity of a man and a woman is 3 : 1 , then find how many days it will take 5 men to complete the same work ?
A. 12 days
B. 15 days
C. 18 days
D. 108 days

Options

A. D
B. B
C. A
D. C

Answer

To solve the problem, we will follow these steps:

### Step 1: Determine the total work done by women
Given that 5 women can complete the work in 36 days, we can find the total work in terms of "woman-days."

Total work = Number of women × Number of days
Total work = 5 women × 36 days = 180 woman-days

### Step 2: Determine the work capacity of one woman
Since we have already calculated the total work in woman-days, we can find the work capacity of one woman.

Work capacity of one woman = Total work / Number of women
Work capacity of one woman = 180 woman-days / 5 women = 36 days

### Step 3: Determine the work capacity of one man
According to the problem, the ratio of the capacity of a man to a woman is 3:1. This means that one man can do the work of 3 women.

Work capacity of one man = 3 × Work capacity of one woman
Work capacity of one man = 3 × (1/36) = 1/12 (in terms of work done per day)

### Step 4: Determine the work capacity of 5 men
Now, we can find the work capacity of 5 men.

Work capacity of 5 men = 5 × Work capacity of one man
Work capacity of 5 men = 5 × (1/12) = 5/12 (in terms of work done per day)

### Step 5: Determine the number of days taken by 5 men to complete the work
To find the number of days taken by 5 men to complete the work, we can use the formula:

Days = Total work / Work capacity of 5 men
Days = 180 woman-days / (5/12) = 180 × (12/5) = 432 days

### Conclusion
Thus, it will take 5 men 12 days to complete the same work.