Banking Quantitative Aptitude Sample Paper Quantitative Aptitude Sample Paper-2

A and B can do a piece of work in 72 days. B and C can do it in 120 days. A and C can do it in 90 days. In how many days, all the three together can do the work?

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

\[=\,\,\frac{2\times (LCM\,\,of\,\,72,\,120\,\,and\,\,90)}{\frac{LCM}{72}+\frac{LCM}{120}+\frac{LCM}{90}}\]

\[=\,\,\frac{2\times (360)}{\frac{360}{72}+\frac{360}{120}+\frac{360}{90}}=\frac{2\times 360}{5+3+4}\]

\[=\frac{2\times 360}{12}=60\,days\]