# In a party if 1 out of every 3 guests brought bouquets,1 out of 5 brought gift items,1 out of 6 gave cash gifts and the remaining 27 guest gave gift vouchers and none of them gave two things. How many people attended the party?

Please find below the solution to the asked query:

Let total number of people attend the party =

*n*, So

From given condition we get

$\frac{n}{3}+\frac{n}{5}+\frac{n}{6}+27=n\phantom{\rule{0ex}{0ex}}\phantom{\rule{0ex}{0ex}}\Rightarrow \frac{{\displaystyle 10n+6n+5n}}{{\displaystyle 30}}+27=n\phantom{\rule{0ex}{0ex}}\phantom{\rule{0ex}{0ex}}\Rightarrow \frac{{\displaystyle 10n+6n+5n+810}}{{\displaystyle 30}}=n\phantom{\rule{0ex}{0ex}}\phantom{\rule{0ex}{0ex}}\Rightarrow \frac{{\displaystyle 21n+810}}{{\displaystyle 30}}=n\phantom{\rule{0ex}{0ex}}\phantom{\rule{0ex}{0ex}}\Rightarrow 21n+810=30n\phantom{\rule{0ex}{0ex}}\phantom{\rule{0ex}{0ex}}\Rightarrow 9n=810\phantom{\rule{0ex}{0ex}}\phantom{\rule{0ex}{0ex}}\Rightarrow n=\frac{{\displaystyle 810}}{9}\phantom{\rule{0ex}{0ex}}\phantom{\rule{0ex}{0ex}}\mathbf{\Rightarrow}\mathit{n}\mathbf{}\mathbf{=}\mathbf{}\mathbf{90}$

Therefore,

**Total number of people attend the party = 90 ( Ans )**

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