Time Work

A and B can do a piece of work in 30 days, while B and C can do the same work in 24 days and C and A in 20 days. They all work together for 10 days when B and C leave. How many days more will A take to finish the work?

  1. 18 days
  2. 24 days
  3. 30 days
  4. 36 days

Answer

Let total work be 120 units  (LCM of 30, 24 and 20).

(A+B)'s one day work = 4 units

(B+C)'s one day work = 5 units

(C+A)'s one day work = 6 units

Adding all three equations and then dividing by 2,

(A+B+C)'s one day work = 7.5 units

A's one day work = 7.5 - 5 = 2.5 units

In 10 days, all three complete 75 units of work. Remaining 45 units can be completed by A in 18 days (at rate of 2.5 units per day).

The correct option is A.