A, B and C can do a piece of work in 24 days, 30 days and 40 days respectively. They began the work together but C left 10 days before the completion of the work. In how many days was the work completed?  Choose the correct choice:
A) 12.5 days  B) 16 days  C) 18 days  D) 11 days  E) 38 days

Rationale: "one day work of a , b and c = 1 / 24 + 1 / 30 + 1 / 40 = 1 / 10 work done by a and b together in the last 10 days = 10 * ( 1 / 24 + 1 / 30 ) = 3 / 4 remaining work = 1 / 4 the number of days required for this initial work = 2.5 days . the total number of days required = 10 + 2.5 = 12.5 days . answer : a"
Answer: A