A) 9 days
B) 5 days
C) 6 days
D) 4 days
Correct Answer: C
Solution :
Let time taken by C to complete to work = x days Time taken by A to complete the work = 3x days And time take by 8 to complete the work \[=\frac{3x}{2}\,days\] According to the question, \[\frac{1}{3x}+\frac{1}{3x}+\frac{1}{x}=1\] \[\Rightarrow \] \[\frac{1}{3x}+\frac{2}{3x}+\frac{1}{x}=1\] \[=\frac{1+2+3}{3x}=1\] \[\Rightarrow \] \[\frac{6}{3x}=1\] \[\Rightarrow \] \[\frac{2}{x}=1\] \[\Rightarrow \] \[x=2\] \[\therefore \] Time taken by \[A=3x=3\times 2=6\] days
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