GATE EC 2016 Set 1 — Question 10
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General Aptitude → Quantitative Aptitude → Time & Work
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Question
P, Q, R and S are working on a project. Q can finish the task in 25 days, working alone for 12 hours a day. R can finish the task in 50 days, working alone for 12 hours per day. Q worked 12 hours a day but took sick leave in the beginning for two days. R worked 18 hours a day on all days. What is the ratio of work done by Q and R after 7 days from the start of the project?
Correct answer
(C) 20:21
Solution
To find the ratio of work done by Q and R after 7 days, we first determine their total work capacities and individual rates.
Rate of Q () = units/hour.
Rate of R () = unit/hour.
Ratio = .
Dividing both sides by 6: .Thus, the correct option is (C).
1.Total work required for Q:
.2.Total work required for R:
.3.Work rates:
Let the total work be units.Rate of Q () = units/hour.
Rate of R () = unit/hour.
4.Work done in 7 days from the start:
- Q took 2 days of sick leave, so Q worked for days.
- Total hours worked by Q = hours.
- Work done by Q () = units.
- R worked for all 7 days at 18 hours/day.
- Total hours worked by R = hours.
- Work done by R () = units.
Ratio = .
Dividing both sides by 6: .Thus, the correct option is (C).
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