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7.Profit and Loss
hard
An article is sold at a profit of $20 \%$. If both the cost price and selling price are $RS.\, 150$ less, profit would be $5 \%$ more. Find the cost price.
A
$750$
B
$650$
C
$950$
D
$850$
Solution
The cost price of the article is $Rs$ $x$.
$\therefore \quad$ The selling price $=₹ \frac{120}{100} \times x$
New cost price $=Rs.(x-150)$
New selling price $=Rs.\left(\frac{120 x}{100}-150\right)$
New profit $\%=\frac{\left(\frac{120 x}{100}-150\right)-(x-150)}{(x-150)} \times 100$
$=\frac{\left(\frac{120 x}{100}-x\right) \times 100}{(x-150)}=\frac{\frac{20 x}{100} \times 100}{x-150}=\frac{20 x}{x-150} \%$
New $\%$ profit $=20+5=25 \%$
$\frac{20 x}{x-150}=25$ or $(x-150) 25=20 x$
$25 x-20 x=150 \times 25$
$5 x=150 \times 25$
$x=150 \times 5=Rs. 750$
Standard 13
Quantitative Aptitude
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