Question
A and B finish a job together in 36 days, while B and C
together finish it in 48 days. The trio completes 75% of the job in 18 days. In how many days will A and C together finish the entire job?Solution
ATQ, Time taken by (A + B + C) for the whole work = 18 / 0.75 = 24 days Let total work = 144 units (LCM of 36, 48, 24) Efficiency of (A + B) = 144 / 36 = 4 units/day Efficiency of (B + C) = 144 / 48 = 3 units/day Efficiency of (A + B + C) = 144 / 24 = 6 units/day Isolate A and C: A = 6 – 3 = 3 units/day C = 6 – 4 = 2 units/day (A + C) = 3 + 2 = 5 units/day Required time = 144 / 5 = 28.8 days
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