Select the correct answerA, B and C can do a work separately in 24, 36 and 48 days respectively. B leaves 7 days before completion and A left 3 days before completion. work will finish in how many days?Options11 5/1312 7/1314 8/1313 9/13

To solve this problem, we first need to find the rate at which A, B, and C work.

1. A's work rate is 1/24 of the work per day (since A can complete the work in 24 days).
2. B's work rate is 1/36 of the work per day (since B can complete the work in 36 days).
3. C's work rate is 1/48 of the work per day (since C can complete the work in 48 days).

Next, we need to find out how much work is done by A, B, and C until B and A leave.

1. B leaves 7 days before completion, so B works for the entire time minus 7 days.
2. A leaves 3 days before completion, so A works for the entire time minus 3 days.
3. C works for the entire time.

Let's denote the total time needed to complete the work as T.

So, the total work done (which is 1, since it's the whole work) can be expressed as:

(1/24)(T-3) + (1/36)(T-7) + (1/48)*T = 1

To solve this equation for T, we first need to find a common denominator for the fractions, which is 288.

So, the equation becomes:

12*(T-3) + 8*(T-7) + 6*T = 288

Solving this equation gives:

12T - 36 + 8T - 56 + 6T = 288 26T - 92 = 288 26T = 380 T = 380 / 26 T = 14 12/26 = 14 8/13

So, the work will be finished in 14 8/13 days.

Therefore, the correct answer is 14 8/13.