If 3 men or 6 women can do a piece of work in 16 days, in how many days can 12 men and 8 women do the same piece of work?

Options

A. 4 days
B. 5 days
C. 3 days
D. 2 days

Answer

To solve the problem, we will follow these steps:

### Step 1: Determine the work done by 3 men and 6 women in one day.
Given that 3 men or 6 women can complete the work in 16 days, we can find the work done by each group in one day.

- Work done by 3 men in one day = 1/16 (since they complete the work in 16 days)
- Work done by 6 women in one day = 1/16

### Step 2: Find the work done by 1 man and 1 woman in one day.
To find the work done by one man and one woman, we can set up the following equations:

- Work done by 1 man in one day = (1/16) / 3 = 1/48
- Work done by 1 woman in one day = (1/16) / 6 = 1/96

### Step 3: Calculate the total work done by 12 men and 8 women in one day.
Now, we can calculate the total work done by 12 men and 8 women in one day.

- Work done by 12 men in one day = 12 * (1/48) = 12/48 = 1/4
- Work done by 8 women in one day = 8 * (1/96) = 8/96 = 1/12

### Step 4: Combine the work done by men and women.
Now we can add the work done by 12 men and 8 women together.

- Total work done in one day = (1/4) + (1/12)

To add these fractions, we need a common denominator. The least common multiple of 4 and 12 is 12.

- (1/4) = 3/12
- (1/12) = 1/12

So,
Total work done in one day = 3/12 + 1/12 = 4/12 = 1/3

### Step 5: Calculate the total days required to complete the work.
If 12 men and 8 women together can do 1/3 of the work in one day, then the total number of days required to complete the work is the reciprocal of the work done in one day.

- Total days = 1 / (1/3) = 3 days

### Final Answer:
Thus, 12 men and 8 women can complete the work in **3 days**.

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