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 12 days before the completion of the work. In how many days was the work completed? Choose the correct option.
A) 13 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 12 days = 12 * ( 1 / 24 + 1 / 30 ) = 9 / 10 remaining work = 1 / 10 the number of days required for this initial work = 1 days . the total number of days required = 12 + 1 = 13 days . answer : a"
Answer: A