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?
- 18 days
- 24 days
- 30 days
- 36 days
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.