Question
A can complete a work in 18 days and B in 24 days. They
work together for 4 days, then C (who alone can complete the work in 36 days) joins them. Find the total time to complete the work.Solution
ATQ, A+B rate = 1/18 + 1/24 = (4+3)/72 = 7/72 work/day Work done in 4 days = 4 × 7/72 = 28/72 = 7/18 Remaining work = 1 − 7/18 = 11/18 A+B+C rate = 1/18 + 1/24 + 1/36 = (4+3+2)/72 = 9/72 = 1/8 Time for remaining = (11/18) ÷ (1/8) = (11/18) × 8 = 44/9 days Total time = 4 + 44/9 = (36/9 + 44/9) = 80/9 days = 8 (8/9) days
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