Question

A man sells an article at a profit of $25$%. If he had bought it at $20$% less and sold it for $Rs.38.75$ less, he would have gained $30$%. Find the cost price of the article.

Answer 1

Let C.P be ${}^{\prime }{x}^{\prime }$

$Profit=25\%$

$S.P=C.P(1+\frac{profit\%}{100})$

$S.P=x(1+\frac{25}{100})$

$=x(1+\frac{1}{4})$

$=\frac{5x}{4}$

If C.P were $20\%$less,

$NewC.P=x(1-\frac{20}{100})$

$=x(1-\frac{1}{5})$

$=\frac{4x}{5}$

$NewS.P=\frac{5x}{4}-38.75$

$\therefore Profit=S.P-C.P=\frac{5x}{4}-38.75-\frac{4x}{5}$

$=\frac{9x}{20}-38.75$

$ATP,nowprofit\%=30\%$

$=>\frac{\frac{9x}{20}-38.75}{\frac{4x}{5}}\times 100=30$

$As,Profit\%=\frac{profit}{C.P}\times 100$

$\frac{9x}{20}-38.75=\frac{30}{100}\times \frac{4x}{5}$

$\frac{9x}{20}-38.75=\frac{6x}{25}$

$\frac{9x}{20}-\frac{6x}{25}=38.75$

$\frac{45x-24x}{100}=38.75$

$21x=3875$

$x=\frac{3875}{21}$

$=184.52\approx 185$

$\therefore C.P=Rs.185$