12 men of 15 women can do a work in 40 days. 8 men and 10 women can do the work in how many days?

Answer

To solve the problem step by step, we will first determine the work done by men and women, and then find how long it will take for 8 men and 10 women to complete the same work.

### Step 1: Determine the work done by 12 men in one day
Given that 12 men can complete the work in 40 days, we can find the work done by 12 men in one day.

\[ \text{Work done by 12 men in 1 day} = \frac{1}{40} \text{ (total work)} \]

### Step 2: Determine the work done by 1 man in one day
To find the work done by 1 man in one day, we divide the work done by 12 men by 12.

\[ \text{Work done by 1 man in 1 day} = \frac{1}{40 \times 12} = \frac{1}{480} \]

### Step 3: Determine the work done by 15 women in one day
We know that 15 women can also complete the work in 40 days. Thus, the work done by 15 women in one day is:

\[ \text{Work done by 15 women in 1 day} = \frac{1}{40} \]

### Step 4: Determine the work done by 1 woman in one day
To find the work done by 1 woman in one day, we divide the work done by 15 women by 15.

\[ \text{Work done by 1 woman in 1 day} = \frac{1}{40 \times 15} = \frac{1}{600} \]

### Step 5: Determine the work done by 8 men and 10 women in one day
Now we will calculate the total work done by 8 men and 10 women in one day.

\[ \text{Work done by 8 men in 1 day} = 8 \times \frac{1}{480} = \frac{8}{480} = \frac{1}{60} \]

\[ \text{Work done by 10 women in 1 day} = 10 \times \frac{1}{600} = \frac{10}{600} = \frac{1}{60} \]

### Step 6: Total work done by 8 men and 10 women in one day
Now, we add the work done by 8 men and 10 women together.

\[ \text{Total work done in 1 day} = \frac{1}{60} + \frac{1}{60} = \frac{2}{60} = \frac{1}{30} \]

### Step 7: Determine the number of days required to complete the work
If 8 men and 10 women can do \(\frac{1}{30}\) of the work in one day, then the total number of days required to complete the work is the reciprocal of the work done in one day.

\[ \text{Number of days} = \frac{1}{\frac{1}{30}} = 30 \text{ days} \]

### Final Answer
8 men and 10 women can complete the work in **30 days**.

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