P alone can finish a piece of work ‘M’ in 9 days while Q takes 3 days to finish it alone. P, Q and R working together can finish the work ‘N’ which is 12 times of work ‘M’ in 9 days. How long will R take to finish work ‘N’, when working alone?
Let the work ‘M’ = 9 units (LCM of 9 and 3) Efficiency of P = 9/9 = 1 units Efficiency of Q = 9/3 = 3 units Efficiency of P, Q and R = (9 × 12)/9 = 12 units per day Efficiency of R = 12 – (1 + 3) = 8 units per day Time taken by R to finish work ‘N’ = 108/8 = 13.5 days
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