10 women can complete the work in 7 days and 10 children take 14 days to complete the work. How many days will 5 women and 10 children will finish the work?

Correct option is C

Given:
10 women can complete the work in 7 days.
10 children can complete the work in 14 days.
Solution:​

Work rate of 10 women
10 women can complete the work in 7 days.
Work rate of 10 women $$= \frac{1}{7}$$​ of the work per day.
Work rate of 10 children:
10 children can complete the work in 14 days.
Work rate of 10 children $$= \frac{1}{14}$$​  of the work per day.
Work rate of 1 woman:
$$\text{Work rate of 1 woman} = \frac{1}{7 \times 10} = \frac{1}{70} \text{ of the work per day}.$$​
Work rate of 1 child:
$$\text{Work rate of 1 child} = \frac{1}{14 \times 10} = \frac{1}{140} \text{ of the work per day}.$$​
Work rate of 5 women:
$$5 \times \frac{1}{70} = \frac{5}{70} = \frac{1}{14} \text{ of the work per day}.$$​
Work rate of 10 children:
$$10 \times \frac{1}{140} = \frac{10}{140} = \frac{1}{14} \text{ of the work per day}.$$​
Combined work rate:
$$\frac{1}{14} + \frac{1}{14} = \frac{2}{14} = \frac{1}{7} \text{ of the work per day}.$$​​
Since the combined work rate is $$\frac{1}{7}$$​of the work per day, the time required to complete the work is:
​$$\text{Time} = \frac{1}{\frac{1}{7}} = 7 \text{ days}.$$​​
5 women and 10 children will finish the work in 7 days.
Alternate Method:

Calculate the total work in terms of woman-days and child-days.
Total work$$= 10 \text{ women} \times 7 \text{ days} = 70 \text{ woman-days}$$​​
Total work =$$10 \text{ children} \times 14 \text{ days} = 140 \text{ child-days}$$​

Combined work rate of 5 women and 10 children:

​$$5 \text{ women} + 10 \text{ children} = 5 \times 1 + 10 \times 0.5 = 10 \text{ units per day}.$$​​
Time required:
$$\text{Time} = \frac{70}{10} = 7 \text{ days}.$$​