Exams › SSC CGL (Prelims) › General

X, Y, and Z can complete a project in 20, 40, and 60 days respectively. X works every day, while Y and Z join X every third day. How long will it take to finish the project?

1. 12 7 2 days
2. 15 5 6 days
3. 16 5 6 days
4. 18 days

Correct answer: 15 5 6 days

Solution

X’s 1-day work = 1/20, Y’s = 1/40, Z’s = 1/60. In 3 days, work done = 1/20 + 1/20 + (1/20+1/40+1/60) = 1/10 + 13/120 = 25/120 = 5/24. So 24/5 = 4.8 such cycles are needed, i.e. 14 full days and 4/5 of the next cycle. The total time comes to 15 5/6 days.

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