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- Standard 13
- Quantitative Aptitude
A trader marked the selling price of an article at $10 \%$ above the cost price. At the time of selling, he allows certain discount and suffers a loss of $1 \% .$ He allowed a discount of $\%$
$9$
$10$
$10.5$
$11$
Solution
Let the cost price of article be $Rs 100.$
$\therefore$ Marked price $=Rs. 110$
Let $x \%$ be the discount given
$\therefore \quad$ S.P. $=110\left(1-\frac{x}{100}\right)$
$\%$ loss $=\frac{\text { C.P. }-\text { S.P. }}{\text { C.P. }} \times 100$
or $100\left(1-\frac{ S.P. }{ C.P. }\right)=1$
or $1-\frac{ S.P. }{ C.P. }=\frac{1}{100}$
or $\frac{S \cdot P}{C \cdot P}=1-\frac{1}{100}=\frac{99}{100}$
i.e. $S.P.$ $=110\left(1-\frac{x}{100}\right)=99$
or $1-\frac{x}{100}=\frac{99}{110}$
or $\frac{x}{100}=1-\frac{99}{110}=\frac{11}{110}=\frac{1}{10}$
or $x=10 \%$
