Question
It takes "Aditi" 12 days alone herself to complete a
task. The differences in efficiency between "Beena" and "Aditi" are 20% and 25%, respectively. "Aditi" and "Beena" begin working together, but 3 days in, "Aditi" leaves. Calculate how long it took "Beena" and "Chinky" working together to complete the remaining tasks.Solution
ATQ, When work is constant, ratio of efficiency is inverse of ratio of time taken. So, ratio of efficiency of 'Aditi' and 'Beena' = 5:6 So, ratio of time taken by 'Aditi' and 'Beena' to finish the work = 6:5 Time taken by 'Beena' alone to finish the work = 12 × (5/6) = 10 days And ratio of efficiency of 'Beena' and 'Chinky' = 4:5 So, ratio of time taken by 'Beena' and 'Chinky' to finish the work = 5:4 Time taken by 'Chinky' alone to finish the work = 10 × (4/5) = 8 days Let, the total work be 120 units {LCM of (8, 10 and 12) } So, efficiency of 'Aditi' = (120/12) = 10 units/day Efficiency of 'Beena' = (120/10) = 12 units/day Efficiency of 'Chinky' = (120/8) = 15 units/day Work done by 'Aditi' and 'Beena' together in 3 days = (10 + 12) × 3 = 66 units Remaining work = 120 - 66 = 54 units So, the time taken by 'Beena' and 'Chinky' together to finish the remaining work = {54/(12 + 15) } = (54/27) = 2 days
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