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. Then, the total number of days Alex would have worked when the job gets finished, is:
Question:
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. Then, the total number of days Alex would have worked when the job gets finished, is:
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. Then, the total number of days Alex would have worked when the job gets finished, is:
Options
Answer: 11
Explanation:
Step 1: Assign daily work Let the work done by Alex in a day = 6x Then, Bob = 3x (half of Alex), Cole = 2x (one-third of Alex) Verify: Bob alone finishes in 40 days → total work = 40 × 3x = 120x Step 2: Work done in the 3-day cycle Day 1 (Alex + Bob) → work = 6x + 3x = 9x Day 2 (Bob + Cole) → work = 3x + 2x = 5x Day 3 (Cole + Alex) → work = 2x + 6x = 8x Total work in one cycle (3 days) = 9x + 5x + 8x = 22x Step 3: Determine number of complete cycles Total work = 120x Work done in 5 complete cycles = 5 × 22x = 110x Remaining work = 120x - 110x = 10x Step 4: Finish remaining work day by day Next cycle Day 1 (Alex + Bob) → work = 9x Remaining after this day = 10x - 9x = 1x Next day (Bob + Cole) → work = 5x, but only 1x left → fraction of day = 1x / 5x = 1/5 day Step 5: Count total days Alex worked In each 3-day cycle, Alex works 2 days (Day 1 and Day 3) Total complete cycles = 5 → Alex works 2 × 5 = 10 days Partial cycle: only Day 1 is a full day Alex works → +1 day Total days Alex worked = 10 + 1 = 11 days
Explanation:
Step 1: Assign daily work Let the work done by Alex in a day = 6x Then, Bob = 3x (half of Alex), Cole = 2x (one-third of Alex) Verify: Bob alone finishes in 40 days → total work = 40 × 3x = 120x Step 2: Work done in the 3-day cycle Day 1 (Alex + Bob) → work = 6x + 3x = 9x Day 2 (Bob + Cole) → work = 3x + 2x = 5x Day 3 (Cole + Alex) → work = 2x + 6x = 8x Total work in one cycle (3 days) = 9x + 5x + 8x = 22x Step 3: Determine number of complete cycles Total work = 120x Work done in 5 complete cycles = 5 × 22x = 110x Remaining work = 120x - 110x = 10x Step 4: Finish remaining work day by day Next cycle Day 1 (Alex + Bob) → work = 9x Remaining after this day = 10x - 9x = 1x Next day (Bob + Cole) → work = 5x, but only 1x left → fraction of day = 1x / 5x = 1/5 day Step 5: Count total days Alex worked In each 3-day cycle, Alex works 2 days (Day 1 and Day 3) Total complete cycles = 5 → Alex works 2 × 5 = 10 days Partial cycle: only Day 1 is a full day Alex works → +1 day Total days Alex worked = 10 + 1 = 11 days
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