15 men can do a job in 12 days and 18 women can do it in 15 days. How many days will 5 men and 3 women take to complete the job ?

Options

A. `28(5/7)`
B. `25 (5/7)`
C. `23 (5/7)`
D. `27 (5/7)`

Answer

To solve the problem, we need to find out how many days 5 men and 3 women will take to complete a job, given that 15 men can do the job in 12 days and 18 women can do it in 15 days.

### Step-by-Step Solution:

1. **Calculate the work done by men in one day:**
- If 15 men can complete the job in 12 days, then the total work can be expressed in man-days.
- Total work = Number of men × Number of days = 15 men × 12 days = 180 man-days.

2. **Calculate the work done by women in one day:**
- If 18 women can complete the job in 15 days, then the total work can also be expressed in woman-days.
- Total work = Number of women × Number of days = 18 women × 15 days = 270 woman-days.

3. **Find the work done by one man and one woman in one day:**
- Work done by one man in one day = Total work / Total man-days = 180 man-days / 15 = 12 man-days per man.
- Work done by one woman in one day = Total work / Total woman-days = 270 woman-days / 18 = 15 woman-days per woman.

4. **Convert the work done by women to man-days:**
- To compare the work done by men and women, we can find the equivalent work done by women in terms of man-days.
- Since 1 man can do the work of 1 woman, we need to find the efficiency ratio.
- Let’s assume the efficiency of a man is M and a woman is W. From the previous calculations, we can set up the equation:
- 15M = 18W
- Therefore, M/W = 18/15 = 6/5.
- This means 1 man is equivalent to 1.2 women in terms of work done.

5. **Calculate the combined work done by 5 men and 3 women in one day:**
- Work done by 5 men in one day = 5 × M.
- Work done by 3 women in one day = 3 × W.
- Using the ratio, we can express the work done by men in terms of women:
- Work done by 5 men = 5 × (5/6)W = (25/6)W.
- Total work done by 5 men and 3 women in one day:
- Total work = (25/6)W + 3W = (25/6)W + (18/6)W = (43/6)W.

6. **Calculate the total time taken by 5 men and 3 women to complete the job:**
- Total work = 270 woman-days (from step 2).
- Time taken = Total work / Work done in one day = 270 / (43/6) = 270 × (6/43) = 270 × 6 / 43 = 1620 / 43 = 37.674 days.

7. **Final Calculation:**
- Rounding off, we can say that it will take approximately 38 days for 5 men and 3 women to complete the job.