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7.Profit and Loss
medium
By selling an article for $Rs.\, 21,$ a man lost such that the percentage loss was equal to the cost price. The cost price of the article was (in $Rs.$)
A
$30,70$
B
$35,60$
C
$45$
D
$50$
Solution
Let, the cost of article be $₹ x .$ At $x \%$ loss, the article sold at $₹ 21$
Now, according to the question, $x\left(\frac{100-x}{100}\right)=21 \Rightarrow x\left(1-\frac{x}{100}\right)=21$
$\Rightarrow x-\frac{x^{2}}{100}=21 \Rightarrow x^{2}-100 x+2100=0$
$\Rightarrow \quad(x-30)(x-70)=0$
$\therefore \quad x=Rs. 30 \quad$ or, $\quad Rs. 70$
Standard 13
Quantitative Aptitude
