‘P’, ‘Q’ and ‘R’ can complete a piece of work in 45 days, 60 days and 75 days respectively. ‘P’ started the work and then ‘Q’ joined him after 15 days. They together worked for 12 days and left the work. Find the time taken by ‘R’ to complete the remaining work.

Let total amount of work = 900 units (LCM of 45, 60 and 75)

Amount of work completed by ‘P’ in one day = 900/45 = 20 units

Amount of work completed by ‘Q’ in one day = 900/60 = 15 units

Amount of work completed by ‘R’ in one day = 900/75 = 12 units

Total amount of work completed by ‘P’ in 15 days = 20 × 15 = 300 units

Amount of work done by ‘P’ and ‘Q’ together in 12 days = 35 × 12 = 420 units

Amount of work left = 900 – 300 – 420 = 180 units

Time taken by ‘R’ to complete 180 units of work = 180/12 = 15 days