GATE EC 2016 Set 2 — Question 5
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General Aptitude → Quantitative Aptitude → Time & Work
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Question
S, M, E and F are working in shifts in a team to finish a project. M works with twice the efficiency of others but for half as many days as E worked. S and M have 6 hour shifts in a day, whereas E and F have 12 hours shifts. What is the ratio of contribution of M to contribution of E in the project?
Correct answer
(B) 1:2
Solution
Let the efficiency of S, E, and F be units/hour.
According to the problem statement, M works with twice the efficiency of others.
So, Efficiency of M () = units/hour.
Efficiency of E () = units/hour.Let the number of days E worked be .
According to the problem statement, M worked for half as many days as E worked.
So, Number of days M worked () = .Shift hours per day:
S and M have 6 hour shifts in a day.
E and F have 12 hour shifts in a day.Total hours worked by M = hours.
Total hours worked by E = hours.Contribution is calculated as Efficiency Total hours worked.Contribution of M () =
units.Contribution of E () =
units.The ratio of contribution of M to contribution of E is:
So, the ratio is 1:2.
According to the problem statement, M works with twice the efficiency of others.
So, Efficiency of M () = units/hour.
Efficiency of E () = units/hour.Let the number of days E worked be .
According to the problem statement, M worked for half as many days as E worked.
So, Number of days M worked () = .Shift hours per day:
S and M have 6 hour shifts in a day.
E and F have 12 hour shifts in a day.Total hours worked by M = hours.
Total hours worked by E = hours.Contribution is calculated as Efficiency Total hours worked.Contribution of M () =
units.Contribution of E () =
units.The ratio of contribution of M to contribution of E is:
So, the ratio is 1:2.
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