3 men or 5 women can do a work in 12 days. How long will 6 men and 5 women take to finish the work?

Options

A. 4 days
B. 5 days
C. 6 days
D. 7 days

Answer

To solve the problem step by step, we can follow these calculations:

### Step 1: Determine the work done by men and women
Given that 3 men or 5 women can complete the work in 12 days, we can first find the work done by one man and one woman in a day.

Let the total work be represented as 1 unit.

- Work done by 3 men in 12 days = 1 unit
- Therefore, work done by 3 men in 1 day = 1/12 units
- Work done by 1 man in 1 day = (1/12) / 3 = 1/36 units

- Work done by 5 women in 12 days = 1 unit
- Therefore, work done by 5 women in 1 day = 1/12 units
- Work done by 1 woman in 1 day = (1/12) / 5 = 1/60 units

### Step 2: Find the combined work done by 6 men and 5 women in one day
Now we need to find the total work done by 6 men and 5 women in one day.

- Work done by 6 men in 1 day = 6 * (1/36) = 6/36 = 1/6 units
- Work done by 5 women in 1 day = 5 * (1/60) = 5/60 = 1/12 units

Now, we can add the work done by 6 men and 5 women together:
- Total work done in one day = (1/6) + (1/12)

To add these fractions, we need a common denominator:
- The common denominator of 6 and 12 is 12.
- (1/6) = 2/12

So,
- Total work done in one day = (2/12) + (1/12) = 3/12 = 1/4 units

### Step 3: Calculate the number of days required to complete the work
If 6 men and 5 women can complete 1/4 of the work in one day, we need to find out how many days it will take to complete 1 unit of work.

Let the number of days required be \( x \):
- Work done in \( x \) days = \( x \times (1/4) = 1 \)

To find \( x \):
- \( x = 1 / (1/4) = 4 \)

### Conclusion
Thus, 6 men and 5 women will take **4 days** to finish the work.

---