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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