Sam can complete a job in 20 days when working alone. Mohit is twice as fast as Sam and thrice as fast as Ayna in the same job. They undertake a job with an arrangement where Sam and Mohit work together on the first day, Sam and Ayna on the second day, Mohit and Ayna on the third day, and this three-day pattern is repeated till the work gets completed. Then, the fraction of total work done by Sam is
Question:
Sam can complete a job in 20 days when working alone. Mohit is twice as fast as Sam and thrice as fast as Ayna in the same job. They undertake a job with an arrangement where Sam and Mohit work together on the first day, Sam and Ayna on the second day, Mohit and Ayna on the third day, and this three-day pattern is repeated till the work gets completed. Then, the fraction of total work done by Sam is
Sam can complete a job in 20 days when working alone. Mohit is twice as fast as Sam and thrice as fast as Ayna in the same job. They undertake a job with an arrangement where Sam and Mohit work together on the first day, Sam and Ayna on the second day, Mohit and Ayna on the third day, and this three-day pattern is repeated till the work gets completed. Then, the fraction of total work done by Sam is
Options
Answer: 3/10
Explanation:
Let the daily work rates be: Mohit = 6k Sam = 3k Ayna = 2k Step 1: Work done in one 3-day cycle Day 1 (Sam + Mohit) = 3k + 6k = 9k Day 2 (Sam + Ayna) = 3k + 2k = 5k Day 3 (Mohit + Ayna) = 6k + 2k = 8k Total work in 1 cycle = 9k + 5k + 8k = 22k Step 2: Work in 2 full cycles (6 days) Total work = 2 × 22k = 44k Total job = 60k → remaining work = 60k − 44k = 16k Day 7 (Sam + Mohit) = 9k → remaining = 16k − 9k = 7k Day 8 (Sam + Ayna) = 5k → remaining = 7k − 5k = 2k Day 9 (Mohit + Ayna) = 2k → job completed Step 3: Total work done by Sam Full cycles: 2 × (Day 1 + Day 2) = 2 × (3k + 3k) = 12k Partial cycle: Day 7 + Day 8 = 3k + 3k = 6k Total by Sam = 12k + 6k = 18k Step 4: Fraction of total work done by Sam Fraction = 18k / 60k = 3/10
Explanation:
Let the daily work rates be: Mohit = 6k Sam = 3k Ayna = 2k Step 1: Work done in one 3-day cycle Day 1 (Sam + Mohit) = 3k + 6k = 9k Day 2 (Sam + Ayna) = 3k + 2k = 5k Day 3 (Mohit + Ayna) = 6k + 2k = 8k Total work in 1 cycle = 9k + 5k + 8k = 22k Step 2: Work in 2 full cycles (6 days) Total work = 2 × 22k = 44k Total job = 60k → remaining work = 60k − 44k = 16k Day 7 (Sam + Mohit) = 9k → remaining = 16k − 9k = 7k Day 8 (Sam + Ayna) = 5k → remaining = 7k − 5k = 2k Day 9 (Mohit + Ayna) = 2k → job completed Step 3: Total work done by Sam Full cycles: 2 × (Day 1 + Day 2) = 2 × (3k + 3k) = 12k Partial cycle: Day 7 + Day 8 = 3k + 3k = 6k Total by Sam = 12k + 6k = 18k Step 4: Fraction of total work done by Sam Fraction = 18k / 60k = 3/10
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