10 men and 8 women can together complete a work in 5 days. Work done by a woman is equal to the half of the work done by a man. In how many days, will 4 men and 6 women complete that work ?

Options

A. 12 days
B. 10 days
C. 8 days
D. 9 days

Answer

To solve the problem step by step, we will use the information given and apply the unitary method.

### Step 1: Determine the work done by men and women
We know that:
- 10 men and 8 women can complete the work in 5 days.
- The work done by a woman is equal to half of the work done by a man.

Let the work done by one man in one day be \( M \) and the work done by one woman in one day be \( W \).
From the information given, we have:
\[ W = \frac{1}{2}M \]

### Step 2: Calculate the total work done in terms of \( M \)
The total work done by 10 men and 8 women in one day can be expressed as:
\[ \text{Total work in one day} = 10M + 8W \]
Substituting \( W \) from the previous step:
\[ 10M + 8\left(\frac{1}{2}M\right) = 10M + 4M = 14M \]

### Step 3: Calculate the total work done in 5 days
Since they can complete the work in 5 days, the total work \( T \) can be calculated as:
\[ T = \text{Total work in one day} \times \text{Number of days} = 14M \times 5 = 70M \]

### Step 4: Determine the efficiency of 4 men and 6 women
Now we need to find out how much work 4 men and 6 women can do in one day.
The work done by 4 men and 6 women in one day is:
\[ \text{Work done by 4 men} = 4M \]
\[ \text{Work done by 6 women} = 6W = 6\left(\frac{1}{2}M\right) = 3M \]
So, the total work done by 4 men and 6 women in one day is:
\[ 4M + 3M = 7M \]

### Step 5: Calculate the number of days required to complete the work
To find the number of days \( D \) required to complete the total work \( T \) with the efficiency of 4 men and 6 women:
\[ D = \frac{T}{\text{Total work done in one day}} = \frac{70M}{7M} = 10 \]

### Conclusion
Thus, 4 men and 6 women will complete the work in **10 days**.

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