Question

By selling an article for $\text{Rs 700,}$the loss is $20\%$.To make a profit of $20\%$,for how much should the article be sold?

Answer 1

Hint: In this problem we need to first find the cost price of an article from the Selling Price of article and loss percentage. We know that Loss $=$Cost Price $-$ Selling Price, we assume cost price as $x$and calculates the loss. But in the problem, they mentioned the loss percentage, so we will calculate the loss percentage by using the below formula and equate both of them to get the value of Cost Price.
Loss Percentage $=\dfrac{\text{Loss}}{\text{Cost Price}}\times 100$
Up to this half of the problem is completed, now we need to calculate the value of the selling price to make a profit of $20\%$. Here we will assume the selling price as $y$ and calculate the profit from assumed selling price and the obtained cost price of the article by using Profit $=$Selling Price $-$ Cost Price. From the value of Profit, we will calculate the value of Profit Percentage from the below formula and equate both of them to get the selling price.
Profit Percentage $=$$\dfrac{\text{Profit}}{\text{Cost Price}}\times 100$

Complete step by step answer:
Given that,
Selling Price of an article is $\text{S}\text{.P}=700$
Loss Percentage is $\text{L }\!\!\%\!\!\text{ }=20\%$
Let the cost price of the article is $\text{C}\text{.P}=x$, then
Loss is
$\begin{align}
  & \text{L}=\text{C}\text{.P}-\text{S}\text{.P} \\
 & \Rightarrow \text{L}=x-700 \\
\end{align}$
Now the loss percentage is
$\begin{align}
  & \text{L}\%=\dfrac{\text{Loss}}{\text{Cost Price}}\times 100 \\
 & \Rightarrow \text{L}\%=\dfrac{x-700}{x}\times 100 \\
\end{align}$
But the loss percentage is $20\%$, then
$\begin{align}
  & \dfrac{x-700}{x}\times 100=20 \\
 & \Rightarrow 100x-70000=20x \\
 & \Rightarrow 100x-20x=70000 \\
 & \Rightarrow 80x=70000 \\
 & \Rightarrow x=\dfrac{70000}{80} \\
 & \Rightarrow x=875 \\
\end{align}$
Hence the cost price of the article is Rs.$875$

Let the selling price of article for which a person will get $20\%$ profit is $\text{S}\text{.}{{\text{P}}_{req}}=x$
Cost Price is $\text{C}\text{.P}=875$
Now profit is
$\begin{align}
  & \text{P}=\text{S}\text{.P}-\text{C}\text{.P} \\
 & \Rightarrow \text{P}=x-875 \\
\end{align}$
Profit percentage is
$\begin{align}
  & \text{P }\!\!\%\!\!\text{ }=\dfrac{\text{Profit}}{\text{Cost Price}}\times 100 \\
 & \Rightarrow \text{P }\!\!\%\!\!\text{ }=\dfrac{x-875}{875}\times 100 \\
\end{align}$
But we have profit percentage as $20\%$, then
$\begin{align}
  & \dfrac{x-875}{875}\times 100=20 \\
 & \Rightarrow 100x-875\times 100=20\times 875 \\
 & \Rightarrow 100x=20\times 875+875\times 100 \\
 & \Rightarrow x=\dfrac{875\left( 20+100 \right)}{100} \\
 & \Rightarrow x=1,050 \\
\end{align}$

Hence the person has to sell the article at a price of Rs.$1,050$ to get a profit of $20\%$.

Note: When we are equating the calculated percentage to the given percentage, don’t write the given percentage in decimals or $\dfrac{\text{Profit Percentage}}{100}$, since we are multiplying $100$ while calculating the percentage, so there is no need to divide the given percentage with $100$.