It takes "Aditi" 12 days alone herself to complete a

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