Question

An article is bought for 12,000 and sold for 13,500. Find the profit percent. Find the price at which it should be sold to make profit of 25%

Answer 1

Answer:

$\underline{\bigstar\:\textbf{Profit Percent on Article :}}$

$:\implies\sf Profit\%=\dfrac{Profit}{CP} \times 100\\\\\\:\implies\sf Profit\%=\dfrac{SP-CP}{CP} \times 100\\\\\\:\implies\sf Profit\%=\dfrac{13500-12000}{12000} \times 100\\\\\\:\implies\sf Profit\% = \dfrac{1500}{12000} \times 100\\\\\\:\implies\sf Profit\% = \dfrac{150000}{12000}\\\\\\:\implies\underline{\boxed{\textsf{ \textbf{Profit\% = 12.5\%}}}}$

$\rule{200}{2}$

$\underline{\bigstar\:\textbf{Required Selling Price :}}$

$:\implies\sf Profit\%=\dfrac{Profit}{CP}\\\\\\:\implies\sf Profit\%=\dfrac{SP-CP}{CP}\\\\\\:\implies\sf 25\%=\dfrac{SP-12000}{12000}\\\\\\:\implies\sf \dfrac{25}{100} = \dfrac{SP - 12000}{12000}\\\\\\:\implies\sf \dfrac{1}{4} = \dfrac{SP - 12000}{12000}\\\\\\:\implies\sf 12000 = 4(SP - 12000)\\\\\\:\implies\sf 12000 = 4SP - (4 \times 12000)\\\\\\:\implies\sf 12000 + (4 \times 12000) = 4SP\\\\\\:\implies\sf 5 \times 12000 = 4SP\\\\\\:\implies\sf \dfrac{5 \times 12000}{4} = SP\\\\\\:\implies\sf 5 \times 3000 = SP\\\\\\:\implies\underline{\boxed{\textsf{ \textbf{SP = Rs. 15,000}}}}$

$\rule{50}{1}\:\sf Or,\:Alternative\:\rule{50}{1}$

$\underline{\bf{\dag}\:\textsf{Profit when rate will be 25\% :}}$

$\dashrightarrow\sf\:\:12.5\%\:of\:Profit=Profit\\\\\\\dashrightarrow\sf\:\:12.5\%\:of\:Profit=SP-CP\\\\\\\dashrightarrow\sf\:\:12.5\%\:of\:Profit=Rs.\:13500-Rs.\:12000\\\\\\\dashrightarrow\sf\:\:12.5\%\:of\:Profit=Rs.\:1500\\\\{\scriptsize\qquad\bf{\dag}\:\:\texttt{Multiplying by 2 Both Sides.}}\\\\\dashrightarrow\sf\:\:(12.5\times2)\%\:of\:Profit=Rs.\:1500\times2\\\\\\\dashrightarrow\sf\:\:25\%\:of\:Profit=Rs.\:3000$

⠀

$\underline{\bf{\dag}\:\textsf{Required Selling Price :}}$

$:\implies\sf SP=CP+Profit\\\\\\:\implies\sf SP=Rs.\:12000+Rs.\:3000\\\\\\:\implies\underline{\boxed{\textsf{ \textbf{SP = Rs. 15,000}}}}$