Question

A mobile phone was marked at 35% above the cost price and a discount of 20% was given at the marked price. Find the profit percent or loss percent made by the shopkeeper.

Answer 1

Hint: We will assume a cost price for the mobile phone. We will calculate the marked price which is $35\%$ above the cost price. Then we will calculate the selling price according to the discount percent given. If the cost price is less than the selling price, we will calculate the profit of the shopkeeper in percentage. And if the cost price is greater than the selling price, we will find out the loss in percentage.

Complete step-by-step solution:
Let the cost price (CP) of the mobile phone be $x$ Rs. The mobile phone was marked at 35% above the cost price. So the marked price (MP) of the mobile phone can be calculated as follows,
\[MP=CP+\dfrac{35}{100}\times CP\]
Substituting $CP=x$, we get
\[\begin{align}
  & MP=x+\dfrac{35}{100}\times x \\
 & =\dfrac{100x+35x}{100} \\
 & =\dfrac{135x}{100}
\end{align}\]
So the marked price is $MP=\dfrac{135x}{100}$. Now, we will calculate the selling price (SP) of the mobile phone. A discount of $20\%$ was given on the marked price while selling it. So the selling price will be calculated as follows,
\[SP=MP-\dfrac{20}{100}\times MP\]
Substituting the value of$MP=\dfrac{135x}{100}$ in the above equation, we get
\[SP=\dfrac{135x}{100}-\left( \dfrac{20}{100}\times \dfrac{135x}{100} \right)\]
Simplifying this equation, we get
\[\begin{align}
  & SP=\dfrac{135x}{100}-\left( \dfrac{1}{5}\times \dfrac{135x}{100} \right) \\
 & =\dfrac{135x}{100}-\left( \dfrac{27x}{100} \right) \\
 & =\dfrac{135x-27x}{100} \\
 & =\dfrac{108x}{100} \\
\end{align}\]
We can write $SP=x+\dfrac{8}{100}x$. As we can see, the selling price is greater than the cost price of the mobile phone. So now, we will calculate the profit of the shopkeeper in percent. Let P be the profit.
We know that $P=SP-CP$. Substituting the values of SP and CP in this equation, we get
\[\begin{align}
  & P=x+\dfrac{8}{100}x-x \\
 & =\dfrac{8}{100}x
\end{align}\]
So, the profit of the shopkeeper is $8\%$ of the cost price.

Note: Calculating the marked price in this question needs to consider a percentage of the cost price. Similarly, while calculating the selling price, we have to subtract the discount percentage of the marked price. So it is important to come up with correct equations to get the correct answer.