Question

Andy and bill together can paint a room in 10 days. Andy alone can complete it in 18 days. If bill paints the room only for half a day daily, then in how many days will andy and bill together compute the work?

Answer 1

Andy can do 1/18 th work  in a day.
Bill and Andy can do 1/10th work in a day.

So Bill can do in a day :  1/10 - 1/18 = 8/180 = 2/45 amount of work

Bill does only half day work.  So Now Bill does 2/45 * 1/2  = 1/45 th work each day.
Total work done now by Andy and Bill together = 1/45 + 1/18 = 7/90 in one day

They can complete work in 90/7 days = 12 + 6/7 days

Answer 2

Rate of doing work = Work / Time taken. Let rate of doing works be A for Andy and B for Bill. Work W can be completed in following ways. W=A(18)=(A+B)(10). This says rate of working of B = A(4/5). This means B can complete a work in 22.5 days. But B works only for half a day, so rate of working of B is halved i.e. W=(B/2)(45). Now total time taken is W=(A+B/2)T. Solving this equation for T using the above ones you get T = 90/7 days