# A man sells an article at a profit of 25%.

Question:

A man sells an article at a profit of 25%. If he had bought it at 20% less and sold it for Rs 36.75 less, he would have gained 30%. Find the cost price of the article.

Solution:

Let the C. P of the article be Rs. $x$.

Original S.P $=x+\frac{25}{100} x$

$=R s . \frac{5 x}{4}$

If he purchased it at $20 \%$ less,

$C . \mathrm{P}=x-\frac{20}{100} x$

$=R s . \frac{4 x}{5}$

He sold the article at Rs $36.75$ less.

So, the selling price $=R s . \frac{5 \mathrm{x}}{4}-36.75$

Given that he would have gained $30 \%$ selling at that price.

Therefore, gain $\%=\frac{\text { s.P-C.P }}{\text { C.P }} \times 100$

S.P $-$ C.P $=\frac{5 x}{4}-36.75-\frac{4 x}{5}$

$=\frac{5 x}{4}-\frac{4 x}{5}-36.75$

$=\frac{25 x-16 x}{20}-36.75$

$=\frac{9 x}{20}-36.75$

So, gain $\%=\frac{\text { S.P-C.P }}{\text { C.P }} \times 100$

$30=\frac{\frac{9 x}{20}-36.75}{\frac{4 x}{5}} \times 100$

$=\left(\frac{9 x}{20}-36.75\right) \times \frac{5}{4 x} \times 100$

$=\frac{9 x-735}{16 x} \times 100$

$30=\frac{9 x-735}{16 x} \times 100$

$\frac{225 x-18375}{4 x}=30$

$225 x-18375=120 x$

$105 x=18375$

$x=\frac{18375}{105}$

$=175$

So, the cost price of the article is Rs. 175 .