A) 80 days
B) 100 days
C) 60 days
D) 150 days
Correct Answer: C
Solution :
[c] \[(A+B)'s\]1 day's work \[=\frac{1}{72}\] |
\[(B\,+C)'s\]1 day's work \[=\frac{1}{120}\] |
\[(A+C)'s\]1 day's work \[=\,\,\frac{1}{90}\] |
\[2\,(A+B+C)=\frac{1}{72}+\frac{1}{120}+\frac{1}{90}\] |
\[=\,\,\frac{5+3+4}{360}=\,\,\frac{1}{30}\] |
\[A+B+C=\frac{1}{30\times 2}=60\,days\] |
Alternate Method |
Time taken by \[(A+B+C)\]to complete the total work |
\[=\,\,\frac{2\times (LCM\,\,of\,\,72,\,120\,\,and\,\,90)}{\frac{LCM}{72}+\frac{LCM}{120}+\frac{LCM}{90}}\] |
\[=\,\,\frac{2\times (360)}{\frac{360}{72}+\frac{360}{120}+\frac{360}{90}}=\frac{2\times 360}{5+3+4}\] |
\[=\frac{2\times 360}{12}=60\,days\] |
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