10 men and 5 women can do a work in 60 days. If one man can do the work of two women, how long will 5 men and 20 woment take to complete half of the work ?

Options

A. 25
B. 30
C. 36
D. 50

Answer

To solve the problem step by step, we will break down the information given and calculate the required time for the work.

### Step 1: Understand the Work Done by Men and Women
We know that:
- 10 men and 5 women can complete the work in 60 days.

Let’s denote:
- The work done by 1 man in 1 day as \( M \).
- The work done by 1 woman in 1 day as \( W \).

### Step 2: Establish Relationships
From the information given:
- 1 man can do the work of 2 women, which means:
\[ M = 2W \]

### Step 3: Calculate Total Work
The total work done by 10 men and 5 women in one day can be expressed as:
\[ 10M + 5W \]
Substituting \( M = 2W \):
\[ 10(2W) + 5W = 20W + 5W = 25W \]

Since they complete the work in 60 days, the total work \( T \) can be calculated as:
\[ T = \text{(Work done in one day)} \times \text{(Number of days)} = 25W \times 60 = 1500W \]

### Step 4: Determine Work Done by 5 Men and 20 Women
Now, we need to find out how much work 5 men and 20 women can do in one day.
The work done by 5 men and 20 women in one day is:
\[ 5M + 20W \]
Substituting \( M = 2W \):
\[ 5(2W) + 20W = 10W + 20W = 30W \]

### Step 5: Calculate the Rate of Work
The rate of work done by 5 men and 20 women in one day is:
\[ \text{Rate} = 30W \]

### Step 6: Find the Time to Complete Half the Work
Half of the total work \( \frac{T}{2} \) is:
\[ \frac{1500W}{2} = 750W \]

Now, to find the number of days \( D \) required to complete half the work:
\[ D = \frac{\text{Half Work}}{\text{Rate}} = \frac{750W}{30W} = 25 \text{ days} \]

### Conclusion
Thus, 5 men and 20 women will take **25 days** to complete half of the work.

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