Question
24 male working 12 hours per day
can finish a piece of work in 30 days, while 36 female working 8 hours per day can finish the same work in 60 days. Which of the following statements is/are correct? I. 12 male and 16 female, working 5 hours a day, will complete the work in 86.4 days. II. If a Manager is 20% more efficient than a female, then 25 Manager and 5 male, working 6 hours a day, will finish the work in 72 days. III. If 5 male and 7 female together finish the work and are paid a total of Rs. 1,360, then the total amount received by the male is Rs. 800.Solution
ATQ, Let the efficiency of a male and a female be 'M' and 'F' units/day, respectively. 24 X 12 X 30 X M = 36 X 8 X 60 X F Or, M:F = 2:1 Let 'M' = '2e' and 'F' = '1e' Total work = 24 X 12 X 30 X 2e = '17,280e' units Statement I: Required time = 17280e Γ· [(12 X 2e + 16 X 1e) X 5] = 86.4 days So, statement I is true. Statement II: Efficiency of a Manager = 1.2 X 1e = '1.2e' Required time = 17280e Γ· [(25 X 1.2e + 5 X 2e) X 6] = 72 days So, statement II is true Statement III: Ratio of amount received by all the male together to that received by all the female together = (5 X 2e) :7e = 10:7 Required amount = (10/17) X 1,360 = Rs. 800 So, statement III is true. Therefore, all statements I, II and III are true.
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