A,B, and C can do a piece of work in 20, 30 and 60 days respectively. In how many days can A do the work if he is assisted by B and C on every third day? A.13 B.14 C.15 D.16 E.17

talaangoshtari wrote:A,B, and C can do a piece of work in 20, 30 and 60 days respectively. In how many days can A do the work if he is assisted by B and C on every third day? A.13 B.14 C.15 D.16 E.17 Let the job = 60 widgets. Since A takes 20 days, A's rate = w/t = 60/20 = 3 widgets per day. Since B takes 30 days, B's rate = w/t = 60/30 = 2 widgets per day. Since C takes 60 days, B's rate = w/t = 60/60 = 1 widget per day. Combined rate for A+B+C working together = 3+2+1 = 6 widgets per day. Over the course of 3 days: Work done by A in the first 2 days = r*t = 3*2 = 6 widgets. Work done by A, B and C on the 3rd day = 6 widgets. Total widgets produced in 3 days = 6+6 = 12 widgets. Since 12 widgets are produced in 3 days, 60 widgets -- 5 times the amount of work -- will take 5 times as long: 5*3 = 15 days. The correct answer is C.

talaangoshtari wrote:A,B, and C can do a piece of work in 20, 30 and 60 days respectively. In how many days can A do the work if he is assisted by B and C on every third day? A.13 B.14 C.15 D.16 E.17 Here's a standard way to do it, in case you weren't to see Mitch's cool idea of using 60 pieces. A takes 20 days to do the work. So he does 1/20 per day. B gets 1/30 done per day. C gets 1/60 done per day. So the rate at which the work gets done is 1/20 on each of two days and 1/20 + 1/30 + 1/60 = 6/60 = 2/20 on every third day. So 1/20 + 1/20 + 2/20 = 4/20 gets done every three days. To get to 20/20 we need 5 x 4/20. So it takes 5 three day periods. 5 x 3 = 15 days. Choose C.