Question
A, B, and C together can do a work alone in 12 days, 18
days, and 54 days respectively. A alone starts the work and work for 3 days and leaves the work, then B alone does the work for 8 days and leaves the work. If remaining work is done by C alone then for how many days has C worked?Solution
Total work = LCM of 12, 18 and 54 = 108 units Unit per day of A = 108/12 = 9 Unit per day of B = 108/18 = 6 Unit per day of C = 108/54 = 2 Units of work done by A in 3 days = 9 × 3 = 27 units Units of work done by B in 8 days = 8 × 6 = 48 units Remaining work = 108 – (27 + 48) = 33 units So, C has worked for 33/2 = 16.5 days
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