Question
‘P’ and ‘Q’ together can complete a work in 30
days. If ‘P’ increases his efficiency by 50% and ‘Q’ decreases his efficiency by 50%, then the total time taken remains unchanged. Find the ratio of efficiencies of ‘P’ and ‘Q’, respectively.Solution
Let the efficiency of ‘P’ and ‘Q’ be ‘x’ units/day and ‘y’ units/day, respectively. So, total work = {(x + y) × 30} units After change in efficiencies, Also, total work = (1.5x + 0.5y) × 30 So, (1.5x + 0.5y) × 30 = (x + y) × 30 Or, 1.5x + 0.5y = x + y Or, 0.5x = 0.5y Or, x : y = 1 : 1 So, ratio of efficiency of ‘P’ and ‘Q’ = 1 : 1
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