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