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- Standard 13
- Quantitative Aptitude
A pen was sold for a certain sum and there was a loss of $20 \% .$ Had it been sold for $Rs.\, 12$ more, there would have been a gain of $30 \% .$ What would be the profit if the pen was sold for $Rs.\, 4.80$ more than what it was sold for? (in $\%$)
$15$
$23$
$29$
no profit, no loss
Solution
Let $CP$ of pen be $Rs.\,x$
and $SP$ be $Rs.\, y$
Initially at loss of $20 \%$
$\Rightarrow \frac{20}{100}=\frac{x-y}{x} \Rightarrow \frac{1}{5} x=x-y \Rightarrow \quad y=\frac{4}{5} x$ $…(i)$
Now if $y$ would change to $Rs.$ $(y + 12),$ then profit becomes $30\%$
$\Rightarrow \frac{30}{100}=\frac{y+12-x}{x} \Rightarrow \frac{3}{10}=\frac{\frac{4}{5} x+12-x}{x}$
$\Rightarrow x=$ $Rs. 24$ $…(ii)$
$y=\operatorname{Rs} \frac{96}{5}$ or $\operatorname{Rs} .19 .2$ $…(iii)$
$\%$ profit now if $y$ becomes $Rs.$ $(y+4.8)$
$\Rightarrow \quad \%$ profit $=\frac{ SP – CP }{ CP } \times 100=\frac{ Rs \cdot( y +4.8)-24}{24} \times 100$
$=\frac{\operatorname{Rs} \cdot(19 \cdot 2+4 \cdot 8)-24}{24} \times 100=0 \%$
