A,B and C needs 8, 12 and 16 days respectively to finish a task. How many days will it take if A works for 2 days then B works on it until 25% of the job is left for C to do, and C completes the work?

One Answer on this Question

1. To solve this problem, we can break it down into steps:

   Step 1: Determine the individual rates of work for A, B, and C.

   If A needs 8 days to finish the task, then their work rate is 1/8 of the task per day.
   If B needs 12 days to finish the task, then their work rate is 1/12 of the task per day.
   If C needs 16 days to finish the task, then their work rate is 1/16 of the task per day.

   Step 2: Calculate the combined work rate of A and B.

   If A works for 2 days, their contribution will be 2 * (1/8) = 1/4 of the task completed.
   If B works until 25% of the job is left for C, then they will complete 75% of the task.

   Step 3: Calculate the time it takes for B to complete 75% of the task.

   Since B’s work rate is 1/12 of the task per day, it will take B (75%)/(1/12) = 9 days to complete 75% of the task.

   Step 4: Calculate the remaining work for C.

   If B completes 75% of the task, then the remaining work for C is 100% – 75% = 25% of the task.

   Step 5: Calculate the time it takes for C to complete the remaining work.

   Since C’s work rate is 1/16 of the task per day, it will take C (25%)/(1/16) = 4 days to complete the remaining 25% of the task.

   Step 6: Calculate the total time required.

   A worked for 2 days, B worked for 9 days, and C worked for 4 days, totaling 2 + 9 + 4 = 15 days.

   Therefore, it will take a total of 15 days for A to work for 2 days, B to work until 25% of the job is left, and C to complete the remaining work.

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