A can do a certain work in 15 days and B can do one-third of the same work in 10 days. A and B work together for 6 days and then A leaves. B completes the remaining work with C in 8 days. A and C together can complete the original work in

B can do the work in = 30 days Let us suppose C can do the same work in x days. Now, A and B can do the part of work in 1 day is. Therefore, A and B can do the work together in 10 days, but they only did for 6 days. and the part of work done in 6 days is =6/10 th part of work. Now, The Remaining work = 1-10/ 6 =2/5 th part of work. Now, according to question B and C did the remaining work in 8 days Hence, in 1 day work done by B and C together is = 1/20th part of work Therefore, one day work of B and C together is =1/ 30 +1/x But it is given =1/ 20 as B and C does 2/5th part of work in 8 days