10 men and 8 women together can complete a work in 5 days. Work done by one woman in a day is equal to half the work done by a man in 1 day. How many days will it take for 4 men and 6 women to complete that work?

Options

A. 12 days
B. 10 days
C. 8 days
D. 4 days

Answer

To solve the problem step by step, we will first determine the total work done in terms of "man-days" and then find out how many days it will take for 4 men and 6 women to complete that work.

### Step 1: Determine the total work done by 10 men and 8 women in 5 days.

Let the work done by one man in one day be \( M \) and the work done by one woman in one day be \( W \).

According to the problem, we know that:
- \( W = \frac{1}{2}M \) (i.e., one woman does half the work of one man)

Now, the total work done by 10 men and 8 women in one day is:
\[ \text{Work done in one day} = 10M + 8W \]
Substituting \( W \):
\[ = 10M + 8 \left(\frac{1}{2}M\right) = 10M + 4M = 14M \]

Since they complete the work in 5 days, the total work \( W_{total} \) is:
\[ W_{total} = \text{Work done in one day} \times \text{Number of days} = 14M \times 5 = 70M \]

### Step 2: Determine the work done by 4 men and 6 women in one day.

Now, we need to find out how much work 4 men and 6 women can do in one day:
\[ \text{Work done in one day by 4 men and 6 women} = 4M + 6W \]
Substituting \( W \):
\[ = 4M + 6 \left(\frac{1}{2}M\right) = 4M + 3M = 7M \]

### Step 3: Calculate the number of days required for 4 men and 6 women to complete the total work.

Now, we need to find the number of days \( D \) it will take for 4 men and 6 women to complete the total work of \( 70M \):
\[ \text{Total work} = \text{Work done in one day} \times \text{Number of days} \]
\[ 70M = 7M \times D \]
Dividing both sides by \( 7M \):
\[ D = \frac{70M}{7M} = 10 \]

### Conclusion

Thus, it will take 4 men and 6 women **10 days** to complete the work.

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