A) 60 days
B) 120 days
C) 80 days
D) 30 days
Correct Answer: B
Solution :
According to the question, Work done by A and B together in one day \[=\frac{1}{10}\]part Work done by B and C together in one day \[=\frac{1}{15}\]part Work done by C and A together in one day \[=\frac{1}{20}\]part By adding all the equations, \[A+B=\frac{1}{10}\] ?(i) \[B+C=\frac{1}{15}\] ?(ii) \[C+A=\frac{1}{20}\] ?(iii) \[2\,\,(A+B+C)=\frac{1}{10}+\frac{1}{15}+\frac{1}{20}\] \[2\,\,(A+B+C)=\frac{6+4+3}{60}=\frac{13}{60}\] \[A+B+C=\frac{13}{20}\] ?(iv) Putting the value of Eq. (i) in Eq. (iv), we get \[\frac{1}{10}+C=\frac{13}{120}\] \[C=\frac{13}{120}-\frac{1}{10}=\frac{13-12}{120}=\frac{1}{120}\] \[\therefore \]Work done in 1 day by C is \[\frac{1}{120}\]part Hence, C will finish the whole work in 120 days.
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