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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