Question

The cost price of an article is Rs 1200 and selling price is $\dfrac{5}{4}$ times of his cost price. Find\[\]
(i) Selling price of the article \[\]
(ii) Profit or Loss as a percentage \[\]

Answer 1

Hint: We first find the selling price SP by multiplying $\dfrac{5}{4}$ to the cost price $CP=1200$ rupees. We find the profit as $\text{P}=\text{SP}-\text{CP}$because we find SP greater than CP. We find the percentage profit using the formula $%P=\dfrac{P}{CP}\times 100$.

Complete step-by-step answer:
We know that cost price abbreviated as CP is the price at which the article is purchased or the amount used to make the article. The selling price abbreviated as SP is the price at which the article is sold. \[\]
The difference between SP and CP is either profit or gain. If SP is greater than CP then the difference between them is profit denoted as P and if CP is larger than SP then the difference then is loss denoted as L. If SP and CP are equal then there is no loss or profit. We have
\[\begin{align}
  & P=SP-CP \\
 & L=CP-SP \\
\end{align}\]
 The percentage profit or loss on the cost price is given by
\[\begin{align}
  & \% P=\dfrac{P}{CP}\times 100 \\
 & \% L=\dfrac{L}{CP}\times 100 \\
\end{align}\]
We are given the question that the cost price CP of the article is 1200 rupees selling price SP is $\dfrac{5}{4}$ times of his cost price.
(i) The selling price SP is $\dfrac{5}{4}$ times his cost price CP. So the selling price in rupee is
\[\text{SP}=\dfrac{5}{4}\times \text{CP=}\dfrac{5}{4}\times 1200=1500\]
 (ii) We observe that the above obtained selling price $\text{SP}=1500$ is greater than cost price $\text{CP}=1200$ rupees which means$\left( SP>CP \right)$. So the profit in rupees is
\[\text{P}=\text{SP}-\text{CP=1500-1200=300}\]
So the percentage profit is
\[ \% P=\dfrac{P}{CP}\times 100=\dfrac{300}{1200}\times 100=25%\]

Note: We can covert selling price and cost price with profit using the formula $\text{CP}=\dfrac{100\times \text{SP}}{100+\text{P}}$. If the seller sells two articles with same selling price one at profit percentage ${{p}_{1}}$ and other at profit percentage ${{p}_{2}}$ then the net percentage $p$ is given by $p=\dfrac{100\left( {{p}_{1}}+{{p}_{2}} \right)+2{{p}_{1}}{{p}_{2}}}{200+{{p}_{1}}+{{p}_{2}}}$