Question : A can do work in 12 days and B in 20 days. If they together work on it for 5 days and the remaining work is completed by C in 3 days, then in how many days can C do the same work alone?
Option 1: 10 days
Option 2: 9 days
Option 3: 12 days
Option 4: 15 days
Correct Answer: 9 days
Solution :
Given: A can do a piece of work in 12 days and B in 15 days.
Time taken by A = 12 days
So, part of work done by A in 1 day = $\frac{1}{12}$
Time taken by B = 20 days
So, part of work done by B in 1 day = $\frac{1}{20}$
Work done (A + B) in 1 day = $\frac{1}{12}+\frac{1}{20}$
⇒ Work done (A + B) in 1 day = $\frac{5+3}{60}=\frac{8}{60}=\frac{2}{15}$
So, work done in 5 days = $\frac{2}{15}×5=\frac{2}{3}$
Remaining work = $1-\frac{2}{3}=\frac{1}{3}$
So, $\frac{1}{3}$ work is done by C in 3 days.
Total work is done by C = 3 × 3 = 9 days
Hence, the correct answer is 9 days.
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