Problem Solving

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.