Question : A, B, and C can do a job working alone in 6, 9, and 18 days, respectively. They all worked together for one day, and then A and B quit. How many days does C working alone take to complete the remainder of the job?
Option 1: 9
Option 2: 6
Option 3: 12
Option 4: 10
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Correct Answer: 12
Solution :
Given: A, B, and C can do a job working alone in 6, 9, and 18 days, respectively.
One day's work for A = $\frac{1}{6}$
B's one day's work = $\frac{1}{9}$
C's one day's work = $\frac{1}{18}$
Let for $x$ days, C worked alone.
A and B each worked for a single day, while C worked for $(x+1)$ days.
According to the question,
$\frac{1}{6}+\frac{1}{9}+\frac{(x+1)}{18}=1$
⇒ $\frac{(x+1)}{18}=\frac{13}{18}$
⇒ $x+1=13$
⇒ $x=12$
So, C worked alone for 12 days.
Hence, the correct answer is 12.
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