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Bob can finish a job in 40 days,if he works alone. Alex is twice as fast as Bob and thrice as fast as Cole in the same job.Suppose Alex and Bob work together on the first day,Bob and Cole work together on the second day,Cole and Alex work together on the third day and then,they continue the work by repeating this three-day roster,with Alex and Bob working together on the fourth day and so on.Then,the total number of days Alex would have worked when the job gets finished,is

Updated On: Jan 15, 2026
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Correct Answer: 11

Solution and Explanation

Given Bob, Alex, and Cole have distinct daily productivity rates, their combined effort is utilized to finish a task. Their individual productivities are established as follows:

  • Bob: 3 units/day
  • Alex: 6 units/day
  • Cole: 2 units/day

Step 1: Total Work Calculation

Bob's capacity to finish the task in 40 days implies the total work required is: \[ 40 \times 3 = 120 \text{ units}. \]

Step 2: Work Achieved in the Initial Three Days

Day 1: Bob and Alex collaborate, completing: \[ 3 + 6 = 9 \text{ units}. \] Day 2: Bob and Cole work together, completing: \[ 3 + 2 = 5 \text{ units}. \] Day 3: Alex and Cole combine efforts, completing: \[ 6 + 2 = 8 \text{ units}. \] The cumulative work accomplished over these three days amounts to: \[ 9 + 5 + 8 = 22 \text{ units}. \]

Step 3: Work Completed in the First 15 Days

The total work completed within the initial 15 days reaches: \[ 22 \times 5 = 110 \text{ units}. \] This leaves 10 units outstanding, necessitating an additional 2 days for completion.

Step 4: Determination of Alex's Working Days

Considering Alex works every 2 out of 3 days, his workdays within the first 15 days are: \[ 10 \text{ days}. \] Alex further contributes on the 16th day to finalize the task. Consequently, Alex's total engagement spans: \[ 10 + 1 = 11 \text{ days}. \]

Final Answer:

Alex's total number of working days is \( \boxed{11} \) days.

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