In how many days can men and women complete the work when working together?
Given statements:
A. The ratio of efficiency of men to women is 3 : 1.
B. Men and child together can complete 1/3 of the work in 9 days.
C. Women can complete 2/3 of the work in 14 days.

Question

Accepted Answer

**Solution:**

1. From statement A, the efficiency ratio of men to women is given as $3 : 1$.

2. Statement C tells us women can complete $ \frac{2}{3} $ of the work in 14 days. Therefore, the total time taken by women to complete the entire work is:

$$\text{Time taken by women} = \frac{14 \times 3}{2} = 21 \text{ days}$$

3. Using the ratio from A, if women take 21 days, men will take:

$$\text{Time taken by men} = \frac{21}{3} = 7 \text{ days}$$

4. Now, the combined efficiency of men and women is:

$$\frac{1}{7} + \frac{1}{21} = \frac{3 + 1}{21} = \frac{4}{21}$$

5. Hence, men and women working together will complete the work in:

$$\frac{21}{4} = 5.25 \text{ days}$$

6. Statement B is not necessary to find the answer.

**Answer:** Only statements A and C together are sufficient to answer the question.

Answer

Answer

Answer

Answer