Question:
X, Y, and Z are three software experts, who work on upgrading the software in a number of identical systems. X takes a day off after every 3 days of work, Y takes a day off after every 4 days of work and Z takes a day off after every 5 days of work.
Starting afresh after a common day off,
i) X and Y working together can complete one new upgrade job in 6 days
ii) Z and X working together can complete two new upgrade jobs in 8 days
iii) Y and Z working together can complete three new upgrade jobs in 12 days If X, Y and Z together start afresh on a new upgrade job (after a common day off), exactly how many days will be required to complete this job?
X, Y, and Z are three software experts, who work on upgrading the software in a number of identical systems. X takes a day off after every 3 days of work, Y takes a day off after every 4 days of work and Z takes a day off after every 5 days of work.
Starting afresh after a common day off,
i) X and Y working together can complete one new upgrade job in 6 days
ii) Z and X working together can complete two new upgrade jobs in 8 days
iii) Y and Z working together can complete three new upgrade jobs in 12 days If X, Y and Z together start afresh on a new upgrade job (after a common day off), exactly how many days will be required to complete this job?
Starting afresh after a common day off,
i) X and Y working together can complete one new upgrade job in 6 days
ii) Z and X working together can complete two new upgrade jobs in 8 days
iii) Y and Z working together can complete three new upgrade jobs in 12 days If X, Y and Z together start afresh on a new upgrade job (after a common day off), exactly how many days will be required to complete this job?
Updated On: Aug 25, 2025
- 3 days
- 4 days
- 2 days
- 3.5 days
- 2.5 days
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Solution and Explanation
To solve this problem, we need to determine how many new upgrade jobs X, Y, and Z can complete together in a single day and use this to find out how many days they will take to complete one job. Here's how we do that:
- Determine each expert's work rate considering their days off:
- X works 3 days and takes 1 day off; thus, he effectively works 75% of the time. Y is effective for 80%, and Z for 80%.
- Given conditions:
- X + Y complete 1 job in 6 days, so their joint work rate is 1/6 jobs per day.
- Z + X complete 2 jobs in 8 days, so their joint work rate is 2/8 = 1/4 jobs per day.
- Y + Z complete 3 jobs in 12 days, so their joint work rate is 3/12 = 1/4 jobs per day.
- Using these equations:
- X + Y = 1/6
- Z + X = 1/4
- Y + Z = 1/4
- Solving these equations simultaneously:
- Add (X + Y), (Z + X), and (Y + Z):
- 2X + 2Y + 2Z = 1/6 + 1/4 + 1/4 = 2/3
- Divide throughout by 2: X + Y + Z = 1/3
- This means X, Y, and Z together can complete one job in 3 days if they work continuously. Considering their actual working day percentages:
- X's effective work rate: 3/4 of the time
- Y's effective work rate: 4/5 of the time
- Z's effective work rate: 4/5 of the time
- Total effective work rate:
- X, Y, Z combined = 1/3 job per day on full efficiency days.
- Effective working rate considering days off = (3/4)*(1/3) + (4/5)*(1/3) + (4/5)*(1/3) = 1/4 + 1/5 + 1/5 = 0.2667+0.2+0.2 = 0.6667 per day.
- Therefore, to complete 1 job, the number of days required = 1/0.6667 ≈ 2.5 days.
Hence, X, Y, and Z working together will complete one job in 2.5 days.
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