Profit and Loss, Finding Selling price

Question

An article was sold at 10% profit. Had it been purchased at Rs 22 more and sold at 5% more, the profit remains same. Find the SP to gain a profit of 62.5%?

Answer 1

Let the Cost Price (CP) be, $x$. Given profit $= 10\%$ , profit in amount = $10\%$ of $x$ $=\frac1{10}\cdot x$

Then CP become $x+22$ and profit is $5\%$ of CP $=$ $\frac{1}{20}\cdot (x+22)$. According to the question profit is same therefore

$\frac{1}{20}\cdot (x+22)=\frac1{10}\cdot x$

Now you get $x$ (CP)$= 22$. Can you take it from here?

Answer 2

Let $c$ be the cost and establish the following relationship from the same profit,

$$10\%\>c = 105\% \cdot110\% \>c - (c+22)$$

Solve for the cost,

$$c = \frac{22}{105\% \cdot110\% - 10\% -1} = 400$$

Then, the selling price for 62.5% profit is 1.625$\times c$.