12 men or 18 women can reap a field in 14 days. The number of days that 8 men and 16 women will take to reap it is…

Options

A. 5
B. 7
C. 8
D. 9

Answer

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

### Step 1: Understand the given information
We know that:
- 12 men can reap a field in 14 days.
- 18 women can also reap the same field in 14 days.

### Step 2: Find the work done by men and women
Let's calculate the work done by 12 men and 18 women in one day.
- Work done by 12 men in one day = \( \frac{1}{14} \) of the field.
- Work done by 18 women in one day = \( \frac{1}{14} \) of the field.

### Step 3: Find the work done by one man and one woman
Now, we can find the work done by one man and one woman:
- Work done by 1 man in one day = \( \frac{1}{14} \div 12 = \frac{1}{168} \) of the field.
- Work done by 1 woman in one day = \( \frac{1}{14} \div 18 = \frac{1}{252} \) of the field.

### Step 4: Calculate the combined work done by 8 men and 16 women
Next, we need to find the total work done by 8 men and 16 women in one day:
- Work done by 8 men in one day = \( 8 \times \frac{1}{168} = \frac{8}{168} = \frac{1}{21} \) of the field.
- Work done by 16 women in one day = \( 16 \times \frac{1}{252} = \frac{16}{252} = \frac{2}{63} \) of the field.

### Step 5: Combine the work done by men and women
Now, we will add the work done by 8 men and 16 women:
- Total work done in one day = \( \frac{1}{21} + \frac{2}{63} \).

To add these fractions, we need a common denominator:
- The least common multiple of 21 and 63 is 63.

Now, convert \( \frac{1}{21} \) to have a denominator of 63:
- \( \frac{1}{21} = \frac{3}{63} \).

So, we have:
- Total work done in one day = \( \frac{3}{63} + \frac{2}{63} = \frac{5}{63} \) of the field.

### Step 6: Calculate the number of days to reap the field
To find the number of days required to reap the entire field, we take the reciprocal of the work done in one day:
- Days required = \( \frac{1}{\frac{5}{63}} = \frac{63}{5} = 12.6 \) days.

### Final Answer
Thus, the number of days that 8 men and 16 women will take to reap the field is **12.6 days**.

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