Numerical answer
A can complete a piece of work in 12 days and B can complete it in 18 days. They work together for 4 days, after which A leaves. C then joins B, and the two finish the remaining work in 3 days. In how many days can C alone complete the entire work?
Show answer and solution
Answer: 10.8
Take total work = 36 units (LCM of 12 and 18). A does 3 units/day, B does 2 units/day.
In 4 days A and B do 4 × 5 = 20 units. Remaining = 16 units.
In the next 3 days B does 3 × 2 = 6 units, so C does 16 − 6 = 10 units in 3 days, i.e. 10/3 units per day.
C alone needs 36 ÷ (10/3) = 108/10 = 10.8 days.
In 4 days A and B do 4 × 5 = 20 units. Remaining = 16 units.
In the next 3 days B does 3 × 2 = 6 units, so C does 16 − 6 = 10 units in 3 days, i.e. 10/3 units per day.
C alone needs 36 ÷ (10/3) = 108/10 = 10.8 days.
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