Final answer:
To find the number of days to complete the whole work, we need to calculate the work done by each person and add them up. A, B, and C complete 1/10th, 1/12th, and 1/15th of the work per day respectively. A left the work 5 days before completion and B left 2 days after A. The total work is the sum of the work done by A, B, and C. The correct answer is d. 7 days.
Step-by-step explanation:
To solve this problem, we need to find the total time taken to complete the work. Let's start by finding the individual rates at which A, B, and C can complete the work. Since A can complete the work in 10 days, we can say that A completes 1/10th of the work per day. Similarly, B completes 1/12th of the work per day and C completes 1/15th of the work per day.
Now, let's calculate the total work done by A in 5 days. Since A completes 1/10th of the work per day, in 5 days A completes 5/10th or 1/2 of the work.
Next, let's calculate the total work done by B. A left the work 5 days before it was completed, which means B worked for 5-2 = 3 days. So, B completes 1/12th x 3 = 1/4th of the work.
Now, let's calculate the total work done by C. Since C completes 1/15th of the work per day, in 15 days C completes 15/15th or the entire work.
Finally, let's add up the work done by A, B, and C to find the total work done. The total work done is 1/2 + 1/4 + 1 = 9/4. So, it takes 9/4 days to complete the whole work, which simplifies to 2 and 1/4 days or 9/4 x 24 = 54 hours.
Therefore, the correct answer is option D) 7 days.