Question
A, B, and C together can do a work alone in 10 days, 45 days, and 90 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 10, 45 and 90 = 90 units Unit per day of A = 90/10 = 9 Unit per day of B = 90/45 = 2 Unit per day of C = 90/90 = 1 Units of work done by A in 3 days = 9 × 3 = 27 units Units of work done by B in 8 days = 8 × 2 = 16 units Remaining work = 90 – (27 + 16) = 47 units So, C has worked for 47/1 = 47 days
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