15 men and 25 men women can dig an area of `880 m^(2)` in 8 days. In how many days can 20 men adn 12 women dig an area of 1040 `m^(2)` , if each man can dig twice the area of the each women can dig in the same amount of time?

Options

A. 6 days
B. 8 days
C. 10 days
D. 2 days

Explanation

To solve the problem step by step, we will first establish the relationship between men and women in terms of work done, and then apply that to find the number of days required for the second group to complete their task.

### Step 1: Understand the work done by men and women
Given:
- 15 men and 25 women can dig 880 m² in 8 days.

Let’s find the total work done in terms of man-days.

**Total work = 880 m²**
**Total man-days = Number of workers × Number of days = (15 + 25) workers × 8 days = 40 workers × 8 days = 320 man-days.**

### Step 2: Calculate the work done per man and per woman
Since we know that each man can dig twice the area of each woman, we can denote:
- Work done by 1 woman in 1 day = W
- Work done by 1 man in 1 day = 2W

Now, we can express the total work done in terms of W:
- Total work done by 15 men and 25 women in 1 day:
- Work by men = 15 men × 2W = 30W
- Work by women = 25 women × W = 25W
- Total work in 1 day = 30W + 25W = 55W

### Step 3: Relate total work to W
Since they complete 880 m² in 8 days:
- Total work in 8 days = 8 days × 55W = 440W
- Therefore, 440W = 880 m² → W = 2 m² (work done by 1 woman in 1 day).

### Step 4: Calculate work done by men
Now, since W = 2 m²:
- Work done by 1 man in 1 day = 2W = 4 m².

### Step 5: Calculate total work done by 20 men and 12 women
Now, we need to find out how many days it takes for 20 men and 12 women to dig 1040 m².

- Work done by 20 men in 1 day = 20 men × 4 m²/man = 80 m².
- Work done by 12 women in 1 day = 12 women × 2 m²/woman = 24 m².
- Total work done by 20 men and 12 women in 1 day = 80 m² + 24 m² = 104 m².

### Step 6: Calculate the number of days required to dig 1040 m²
Now, we can find the number of days (D) required to dig 1040 m²:
- Total work = 1040 m²
- Work done in 1 day = 104 m²

Thus, the number of days required:
\[ D = \frac{Total \, work}{Work \, done \, in \, 1 \, day} = \frac{1040 \, m²}{104 \, m²/day} = 10 \, days. \]

### Final Answer
The number of days required for 20 men and 12 women to dig 1040 m² is **10 days**.

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