Question
A, B and C can complete a work in 15, 20 and 30 days
respectively. They all start working together. After 3 days, C leaves. The remaining work is completed by A and B together. In how many total days is the work finished?Solution
A’s 1-day work = 1/15 B’s 1-day work = 1/20 C’s 1-day work = 1/30 Work done in first 3 days by A+B+C: Daily work = 1/15 + 1/20 + 1/30 LCM(15,20,30)=60 1/15=4/60, 1/20=3/60, 1/30=2/60 Total per day = 9/60 = 3/20 In 3 days: 3 × 3/20 = 9/20 Remaining work = 1 − 9/20 = 11/20 Now only A and B work: A+B per day = 1/15 + 1/20 = (4+3)/60 = 7/60 Time to finish remaining work: (11/20) ÷ (7/60) = (11/20) × (60/7) = (11×3)/7 = 33/7 days Total time = 3 + 33/7 = (21+33)/7 = 54/7 days
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