Single correct option
Machines X, Y and Z, working together, can complete a production job in 6 days. X and Y together can complete it in 10 days, and Y and Z together can complete it in 12 days. Working alone, how many days will Z take to complete the job?
- A. 12
- B. 15
- C. 18
- D. 20
Show answer and solution
Answer: (B) 15
Let the daily rates be x, y, z (fraction of job per day). x + y + z = 1/6.
Since x + y = 1/10, we get z = 1/6 − 1/10 = 5/30 − 3/30 = 1/15 of the job per day.
So Z alone takes 1/z = 15 days.
(Check: since y + z = 1/12, x = 1/6 − 1/12 = 1/12, so X takes 12 days; then y = 1/6 − 1/12 − 1/15 = 10/60 − 5/60 − 4/60 = 1/60, so Y takes 60 days — and X&Y together give 1/12 + 1/60 = 5/60 + 1/60 = 1/10 ✓.)
Tip: Adding all three pair-sums gives 2(x+y+z); here it's cleaner to just isolate each machine directly from the total and one pair-sum.
Since x + y = 1/10, we get z = 1/6 − 1/10 = 5/30 − 3/30 = 1/15 of the job per day.
So Z alone takes 1/z = 15 days.
(Check: since y + z = 1/12, x = 1/6 − 1/12 = 1/12, so X takes 12 days; then y = 1/6 − 1/12 − 1/15 = 10/60 − 5/60 − 4/60 = 1/60, so Y takes 60 days — and X&Y together give 1/12 + 1/60 = 5/60 + 1/60 = 1/10 ✓.)
Tip: Adding all three pair-sums gives 2(x+y+z); here it's cleaner to just isolate each machine directly from the total and one pair-sum.
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