A can do as much work in 3 days as B can do in 5 days and B can do as much work in 2 days as C can do in 3 days. All of them together can do a certain piece of work in 20 days. The no. of days A alone take to do the work will be :

Explanation

Ratio of ability of `A` and `B` to do a piece of work `= 5:3`

Ratio of ability of `B` and `C` to do a piece of work `= 3:2`

`:.` Ratio of ability of `A` and `C` to do a piece of work `= 5:2`

`:.` Ratio of ability of `A`,`B` and `C` to do a piece of work = `5:3:2`

Together `A,B and C` complete a certain work in `20` days.

So, time taken by `A` to complete that work alone `= (5+3+2)/5**20 = 10/5**20 = 40` days