A, B and C can do a work in 20 days, 24 days and 30 days respectively. A and B left the work 4 days before completion of the work, then whole work will finish in how many days?Options10 14/1512 7/1511 8/159 2/3

Sure, let's solve this step by step:

1. First, we need to find the one day's work of A, B, and C.

   A's one day work = 1/20 B's one day work = 1/24 C's one day work = 1/30

2. Now, let's find the combined one day's work of A, B, and C.

   (A+B+C)'s one day work = 1/20 + 1/24 + 1/30 = (6 + 5 + 4)/120 = 15/120 = 1/8

   So, A, B, and C together can finish the work in 8 days.

3. But A and B left the work 4 days before completion. So, for the first (8-4)=4 days, A, B, and C worked together. And for the last 4 days, only C worked.

4. The work done in the first 4 days = 4 * (1/8) = 1/2 (since A, B, and C together can do 1/8 of the work in a day)

5. The remaining work = 1 - 1/2 = 1/2 (since the total work is considered as 1)

6. Now, let's find out how many days C will take to complete the remaining work.

   As C's one day work is 1/30, to complete 1/2 work, C will take (1/2) / (1/30) = 15 days.

7. So, the total time to finish the work = 4 (days A, B, C worked together) + 15 (days C worked alone) = 19 days.

So, the whole work will be finished in 19 days. But this option is not given in the question. There might be a mistake in the question or the options provided.