8 men and 12 boys can finish a work in 10 days while 6 men and 8 boys can finish it in 14 days. Find the time taken by one man alone and that by one boy alone to finish the work.

Explanation

Let one man alone can finish the work in `{x}` days and one boy alone can finish the work in` y `days.



In one day man can do `\frac{1}{{x}}` th work, then 8 man can do `\frac{8}{{x}}` th part of work. In one day man can do `\frac{1}{y}` th work, then `8 `man can do `\frac{12}{y}` th part of work. Given together they can finish in `10 `days


`\therefore \frac{8}{{x}}+\frac{12}{{y}}=\frac{1}{10}`


Again `6` man can do in one day `=\frac{6}{x}` parts of the work.

...