Question

A trader sold an article at a profit of 18 % . Had it been sold for 222 more, he would have got a profit of 22 % . What is the cost price of the article ? ​

Answer 1

$\mathfrak{Answer:}$

= Rs. 5550.

$\mathfrak{Step-by-Step\;Explanation:}$

$\underline{\bold{Given\;in\;the\;Question:}}$

• A trader sold an article at a profit of 18 % .
• It had been sold for 222 more, he would have got a profit of 22 %.

Let the cost price of an article be Rs. x.

$\bigstar\quad\textbf{We know that : \boxed{\bold{Selling\;Price=CP\left(\dfrac{100+P\%}{100}}\right)^}}\\\\\\\bullet\quad\textbf{If the profit\% is 18\% then SP :}\\\\\\\tt{=x\left(\dfrac{100+18}{100}\right)}\\\\\\\tt{=x\times\dfrac{118}{100}=Rs.\dfrac{118x}{100}.}$

$\bullet\quad\textbf{If the profit\% is 22\% then SP :}\\\\\\\tt{=x\left(\dfrac{100+22}{100}\right)}\\\\\\\tt{=x\times\dfrac{122}{100}=Rs.\dfrac{122x}{100}.}$

$\mathfrak{According\:to\:Question:}\\\\\\\implies\tt{\dfrac{122x}{100}-\dfrac{118x}{100}=222}\\\\\\\implies\tt{\dfrac{122x-118x}{100}=222}\\\\\\\implies\tt{4x=22200}\\\\\\\implies\tt{x=\dfrac{22200}{4}}\\\\\\\therefore\quad\tt{x=5550.}$

$\boxed{\boxed{\bold{Cost\;Price\;of\;the\;article=Rs.5550.}}}$