If 12 women can complete a work in 64 days, then in how many days will 16 women complete two-thirds of the work?

Correct option is C

Given:

- 12 women can complete the work in 64 days.
- We need to determine how many days 16 women will take to complete two-thirds of the work.

Formula Used:
1. Total Work in Woman-Days:

Total Work = $$\text{Number of women} \times \text{Number of days}$$​​


2. Work for Two-Thirds of the Total Work:

Work for two-thirds = $$\frac{2}{3} \times \text{Total Work}$$​​


3. Time to Complete the Work for 16 Women:

Time (Days) = $$\frac{\text{Work to be completed}}{\text{Number of women}}$$​​


Solution:
1. Calculate the total work in terms of woman-days:

Total Work = $$12 \times 64 = 768 \text{ woman-days}$$​​

This means the total work requires 768 woman-days to complete.

2. Calculate two-thirds of the total work:

Work for two-thirds = $$\frac{2}{3} \times 768 = 512 \text{ woman-days}$$​​


3. Calculate the number of days for 16 women to complete 512 woman-days of work:

Time (Days) = $$\frac{512}{16} = 32 \text{ days}$$​​


Final Answer:
16 women will complete two-thirds of the work in 32 days.