# In an examination, a girl secures 42% and passes the examination by 7 marks, find maximum & minimum marks of the examination if the cutoff is 40%.

$\begin{array}{l}\text{Given that,}\\ \text{Girl marks secures }=42\%\ \\ \text{Minimum marks }=40\ \%\\ \text{Let Maximum marks secured}=a\\ \text{so,}\\ \text{girl secured 7 more marks then minimum}\\ \text{So,}\ a\times\frac{42}{100}=a\times\frac{40}{100}+7\\ \Rightarrow a\left(\frac{42}{100}-\frac{40}{100}\right)=7\\ \Rightarrow a=\frac{\left(7\times100\right)}{2}=350\ \\ \text{so, maximum marks is 350.}\\ \text{minimum marks is}=350\ \times\frac{40}{100}=140\end{array}$

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