If 4 men or 6 women can do a piece of work in 12 days working 7 hours a day. How many days will it take to complete a work twice as large with 10 men and 3 women working together 8 hours a day ?

Question

Accepted Answer

To determine how many days it will take to complete a work twice as large with 10 men and 3 women working together 8 hours a day, we need to follow a systematic approach based on the given information.

### Step-by-Step Explanation:

1. **Understanding the Work Capacity:**
   - 4 men can complete the work in 12 days working 7 hours a day.
   - Similarly, 6 women can complete the same work in 12 days working 7 hours a day.

2. **Calculate Total Work in Man-Hours:**
   - For 4 men: Total work = 4 men × 12 days × 7 hours/day = 336 man-hours.
   - For 6 women: Total work = 6 women × 12 days × 7 hours/day = 504 woman-hours.

3. **Equating Man-Hours and Woman-Hours:**
   - Since both 4 men and 6 women can complete the same work, 336 man-hours = 504 woman-hours.
   - Therefore, 1 man-hour = 504/336 woman-hours = 1.5 woman-hours.

4. **Calculate Work for Twice the Size:**
   - The work is twice as large, so total work = 2 × 336 man-hours = 672 man-hours.

5. **Calculate Combined Work Capacity of 10 Men and 3 Women:**
   - 10 men working 8 hours a day = 10 men × 8 hours = 80 man-hours per day.
   - 3 women working 8 hours a day = 3 women × 8 hours = 24 woman-hours per day.
   - Convert woman-hours to man-hours: 24 woman-hours = 24/1.5 = 16 man-hours.
   - Total work capacity per day = 80 man-hours (from men) + 16 man-hours (from women) = 96 man-hours per day.

6. **Calculate Number of Days Required:**
   - Total work required = 672 man-hours.
   - Days required = Total work / Work capacity per day = 672 man-hours / 96 man-hours per day = 7 days.

### Conclusion:

- **Option 2 (7 days) is correct** because the calculations show that it will take 7 days for 10 men and 3 women working together 8 hours a day to complete the work that is twice as large.

### Explanation of Incorrect Options:

- **Option 1 (6 days):** This option is incorrect because the calculated number of days required is 7, not 6. The work capacity per day does not allow for completion in 6 days.
- **Option 3 (8 days):** This option is incorrect because the work can be completed in fewer days (7 days) given the work capacity per day.
- **Option 4 (9 days):** This option is incorrect because the work can be completed in fewer days (7 days) given the work capacity per day.

By following the logical steps and calculations, we confirm that Option 2 is indeed the correct answer.