Question

8 men and 12 boys can finish a piece of work in 10 days while 6 men and 8 boys can finish it in 10 days find the time taken by 1 men and 1 boys alone to finish the work

Answer 1

Let x be the days taken by 1 man to finish the entire work.
Then work done by 1 man in 1 day = 1/x

Let y the days taken by 1 boy to finish the entire work.
Then work done by 1 boy in 1 day = 1/x

From the question,
8(1/x) + 12(1/y) = 1/10........eq(1)

6(1/x) + 8(1/y) = 1/10 ........eq(2)

By solving this equation You will get your answer..
How ever the question you have given has an error..