Question
‘X’ and ‘Y’ together can do a work in 16 days.
If ‘X’ increases his efficiency by 75% and ‘Y’ decreases his efficiency by 25%, then the time taken to complete the work remains unchanged. Find the ratio of efficiencies of ‘X’ and ‘Y’, respectively.Solution
Let the efficiency of ‘X’ and ‘Y’ be ‘x’ units/day and ‘y’ units/day, respectively. So, total work = {(x + y) × 16} units After change in efficiencies, Also, total work = (1.75x + 0.75y) × 16 So,
1.75x + 0.75y = x + y Or,
0.75x = 0.25y Or,
x : y = 3 : 1 So, ratio of efficiency of ‘X’ and ‘Y’ = 3 : 1
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