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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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Solution and Explanation

Bob, Alex, and Cole collaborate on a task with specific work rates. The objective is to ascertain the number of days Alex contributes until the task is finished.

Step 1: Determine Efficiencies

Bob's efficiency is established at 3 units/day. Consequently:

  • Alex's efficiency = 6 units/day
  • Cole's efficiency = 2 units/day

Bob, working alone, completes the task in 40 days. The total work required is calculated as: \[ \text{Total work} = 40 \times 3 = 120 \text{ units} \]

Step 2: Work Cycle (3-Day Repeating Pattern)

The work accomplished during each of the initial three days (a single cycle) is defined as follows:

  1. Day 1: Alex and Bob collaborate, completing \(6 + 3 = 9\) units.
  2. Day 2: Bob and Cole collaborate, completing \(3 + 2 = 5\) units.
  3. Day 3: Alex and Cole collaborate, completing \(6 + 2 = 8\) units.

The total work completed within one 3-day cycle is the sum of these daily contributions: \[ 9 + 5 + 8 = 22 \text{ units} \] Therefore, 22 units of work are completed every 3 days.

Step 3: Work Completed in First 15 Days

Fifteen days equate to 5 full 3-day cycles. The total work completed during this period is: \[ \text{15 days} = 5 \text{ cycles} \Rightarrow 5 \times 22 = 110 \text{ units} \] The remaining work to be completed is: \(120 - 110 = 10\) units.

Step 4: Day-by-Day After 15 Days

Day 16: Alex and Bob work together, completing 6 + 3 = 9 units. The cumulative work reaches 119 units.
Day 17: Bob and Cole work together, completing 3 + 2 = 5 units. This contribution exceeds the remaining work, thus completing the task. The task is finalized on Day 17.

Step 5: Count How Many Days Alex Worked

Alex participates in work on the following days:

  • Days 1, 3, 4, 6, 7, 9, 10, 12, 13, and 15. This accounts for 10 days within the first 15 days.
  • Day 16, when Alex collaborates with Bob.

Alex's total contribution spans 11 days. \[ \boxed{\text{Alex worked for 11 days in total}} \]

Final Answer:

\[ \boxed{11} \]

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The passage given below is followed by four summaries. Choose the option that best captures the essence of the passage.
In the dynamic realm of creativity, artists often find themselves at the crossroads between drawing inspiration from diverse cultures and inadvertently crossing into the territory of cultural appropriation. Inspiration is the lifeblood of creativity, driving artists to create works that resonate across borders. In a globalized era of the modern world, artists draw from a vast array of cultural influences. When approached respectfully, inspiration becomes a bridge, fostering understanding and appreciation of cultural diversity. However, the line between inspiration and cultural appropriation can be thin and easily blurred.
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