10 skilled persons can complete a work in 8 days and 10 semi-skilled persons take 12
days to complete the work. How many days will 4 skilled persons and 6 semi-skilled persons together take to complete the work?

Correct option is D

Given
10 skilled persons complete the work in 8 days
10 semi-skilled persons complete the work in 12 days
Required group: 4 skilled + 6 semi-skilled

Formula Used
Work = Men × Days
Efficiency (1 Day Work) = $$\frac{1}{\text{Total Days Required}}$$​​

Solution
1 skilled person's 1 day work =$$\frac{1}{10 \times 8} = \frac{1}{80}$$​​
1 semi-skilled person's 1 day work = $$\frac{1}{10 \times 12} = \frac{1}{120}$$​​
Work done by 4 skilled and 6 semi-skilled persons in 1 day:
​$$= 4 \times \frac{1}{80} + 6 \times \frac{1}{120}\\\ \\= \frac{1}{20} + \frac{1}{20}\\\ \\= \frac{2}{20} = \frac{1}{10}\\\ \\$$​​
Since their combined 1 day work is $$\frac{1}{10}$$​, they will complete the total work in 10 days.

Final Answer
So the correct answer is (d)