Question
‘X’ is 25% more efficient than ‘Y’, and ‘Z’
is 25% less efficient than ‘Y’. Together, they can complete a job in 40 days. If X and Y work together for 30 days, how long will Z take to finish the remaining work?Solution
Let efficiency of ‘Y’ be ‘x’ units/day Efficiency of ‘X’ = 1.25x units/day Efficiency of ‘Z’ = 0.75x units/day Total work = (1.25x + x + 0.75x) × 40 = 120x units Work done by X and Y in 30 days = 30 × (1.25x + x) = 67.5x units Remaining work = 120x – 67.5x = 52.5x units Time taken by Z = 52.5x ÷ 0.75x = 70 days
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