A job can be completed by 6 men and 8 women in 10 days. 26 men and 48 women can finish the same work in 2 days. 15 men and 20 women can do the same work in - days.

Options

A. 4 days
B. 6 days
C. 2 days
D. 8 days

Answer

To solve the problem step by step, we need to establish the work rates of men and women based on the information given in the question.

### Step 1: Determine the total work done by 6 men and 8 women in 10 days.

Let the work done by 1 man in 1 day be \( M \) and the work done by 1 woman in 1 day be \( W \).

From the first condition:
- 6 men and 8 women can complete the work in 10 days.

The total work \( W \) can be expressed as:
\[ W = (6M + 8W) \times 10 \]

### Step 2: Determine the total work done by 26 men and 48 women in 2 days.

From the second condition:
- 26 men and 48 women can complete the work in 2 days.

The total work \( W \) can also be expressed as:
\[ W = (26M + 48W) \times 2 \]

### Step 3: Set the two expressions for total work equal to each other.

From Step 1 and Step 2, we have:
\[ (6M + 8W) \times 10 = (26M + 48W) \times 2 \]

### Step 4: Simplify the equation.

Expanding both sides:
\[ 60M + 80W = 52M + 96W \]

Rearranging gives:
\[ 60M - 52M = 96W - 80W \]
\[ 8M = 16W \]

### Step 5: Find the ratio of men to women.

Dividing both sides by 8:
\[ M = 2W \]

This means the ratio of men to women is:
\[ \frac{M}{W} = \frac{2}{1} \]

### Step 6: Use the ratio to find the work done by 15 men and 20 women.

Now we need to find out how many days it will take for 15 men and 20 women to complete the work.

Using the ratio \( M = 2W \):
- Work done by 15 men in one day is \( 15M = 15 \times 2W = 30W \).
- Work done by 20 women in one day is \( 20W \).

Thus, the total work done by 15 men and 20 women in one day is:
\[ 30W + 20W = 50W \]

### Step 7: Calculate the total work \( W \).

From the first condition, we can find \( W \):
\[ W = (6M + 8W) \times 10 \]
Substituting \( M = 2W \):
\[ W = (6 \times 2W + 8W) \times 10 \]
\[ W = (12W + 8W) \times 10 = 20W \times 10 = 200W \]

### Step 8: Calculate the number of days for 15 men and 20 women to complete the work.

Now, we can find the number of days \( D \) it takes for 15 men and 20 women to complete the work:
\[ D = \frac{Total \ Work}{Work \ per \ day} = \frac{200W}{50W} = 4 \text{ days} \]

### Final Answer:
The number of days it will take for 15 men and 20 women to complete the work is **4 days**.

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