Question
βAβ and βBβ together can complete a work in 18
days. If βAβ increases his efficiency by 20% and βBβ decreases his efficiency by 40%, then the time required to complete the work remains unchanged. Find the ratio of efficiencies of βAβ and βBβ, respectively.Solution
Let the efficiency of βAβ and βBβ be βxβ units/day and βyβ units/day, respectively. So, total work = {(x + y) Γ 18} units After change in efficiencies, Also, total work = (1.2x + 0.6y) Γ 18 So,
1.2x + 0.6y = x + y Or,
0.2x = 0.4y Or,
x : y = 2 : 1 So, ratio of efficiency of βAβ and βBβ = 2 : 1
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