Question

A shopkeeper sold an article offering a discount of \[5\%\] and earned a profit of \[23.5\%\]. What would have been the percentage of profit earned if no discount was offered ?
A). \[24.5\%\]
B). \[25\%\]
C). \[28.5\%\]
D). \[30\%\]

Answer 1

Hint: In this question, given that a shopkeeper sold an article with the discount of \[5\%\] and he earned \[23.5\%\] profit. We need to find the percentage of the profit earned when no discount was offered. Since the cost price of the article is not mentioned in the question, we need to assume the cost price.
Formula used :
\[\text{Profit} = \text{Selling price} – \text{Cost price}\]
The formula to find the profit percent is
\[Profit\ percent\ = \dfrac{\text{Profit}}{\text{Cost price}}\ \times 100\]

Complete step-by-step solution:
Let us set a value for the cost price of the article as \[Rs.\ 100\]
Let the marked price be \[x\]
Given,
\[\text{Discount percent} = 5\%\]
\[S.P = 100 – 5 = 95\]
\[\text{Profit percent} = 23.5\%\]
From the formula,
\[\text{Profit} = \text{Selling price} – \text{Cost price}\]
We can find the selling price.
\[\text{Selling price} = \text{Profit} + \text{Cost price}\]
By substituting the values,
We get,
\[S.P = 23.5 + 100\]
By adding,
We get,
\[S.P = Rs.123.5\]
Now ,
The marked price ,( M. P)
\[\dfrac{95}{100} \times x = 123.5\]
By cross multiplying,
We get,
\[x = \dfrac{123.5 \times 100}{95}\]
By simplifying,
We get,
\[x = Rs.130\]
Therefore the selling price of the article is \[Rs.130\]
Now we need calculate the profit attained,
\[\text{Profit obtained} = \ selling\ price – cost\ price\]
By substituting the values,
We get,
 \[\text{Profit obtained} = 130 – 100\]
By subtracting,
We get,
\[\text{Profit obtained} = Rs.30\]
Now we can calculate the percentage profit,
\[\text{Profit percentage} = \dfrac{{Profit}}{{cost\ price\ }} \times 100\]
By substituting the value,
\[\text{Profit percentage} = \dfrac{30}{100} \times 100\]
By simplifying,
We get,
\[\text{Profit percentage} = 30\%\]
Thus the percentage of the profit earned is \[30\%\]
Final answer :
The percentage of the profit earned is \[30\%\]
Option D). \[30\%\].

Note: If our expenses are less than the money we earn, that is known as Profit. Profit is determined by subtracting total income and the expenses. Similarly if our expenses are greater than our incomes that is known as loss. The formula used to calculate the loss percent is \[Loss\ \% = \ \dfrac{{Loss}}{{Cost}{\ price\ }} \times 100\]