Question

A shopkeeper sold a TV set for Rs. 17,940 with a discount of 8% and earned a profit of 19.6%. What would have been the percentage of profit earned if no discount was offered?
A. 24.8%
B. 25%
C. 26.4%
D. Cannot be determined
E. None of these

Answer 1

Hint: To solve this question, we will first find the marked price of the TV set and then find the cost price. We will then calculate the profit by subtracting the cost price from the marked price and calculate the profit percentage by using the formula, $\text{Profit}\%=\dfrac{\text{Profit}}{\text{Cost price}}\times 100$.

Complete step-by-step answer:

It is given in the question that a shopkeeper sold a TV set for Rs. 17,940 with a discount of 8% and earned a profit of 19.6% and we have been asked to find the gain percentage if no discount is offered. The selling price of the TV set is Rs. 17,940, the discount offered is 8%. Let us assume the marked price as X. So, the marked price can be calculated as, 92% of X = 17,940. We are taking 92% of X, because we are assuming marked price as 100% and so, 17,940 will be 92% of the marked price. So, we get,
$\begin{align}
  & \dfrac{92}{100}X=17940 \\
 & \Rightarrow 92X=1794000 \\
 & \Rightarrow X=\dfrac{1794000}{92} \\
 & \Rightarrow X=19500 \\
\end{align}$
So, we get the marked price of the TV set as Rs. 19,500. Now, it is given that the shopkeeper gained 19.6% on it, so the cost price of the TV will be $\dfrac{\text{Selling price}\times 100}{100+\left( \text{profit percentage} \right)}$. We know that the selling price of the TV set is Rs. 17,940 and that the profit percentage is 16.9%. So, we will get the cost price, CP as,
$\begin{align}
  & =\dfrac{17940\times 100}{100+19.6} \\
 & \Rightarrow \dfrac{1794000}{119.6} \\
 & \Rightarrow 15000 \\
\end{align}$
So, we get the cost price of the TV as Rs. 15,000. The profit gained by the shopkeeper if he had not offered any discount would be = (Marked price - Cost price). So, we will get the profit as, 19500 - 15000 = Rs. 4500. Now, we can calculate the profit percentage by using the formula, $\text{Profit}\%=\dfrac{\text{Profit}}{\text{Cost price}}\times 100$. So, we get,
$\begin{align}
  & =\dfrac{4500}{15000}\times 100 \\
 & \Rightarrow 30 \\
\end{align}$
So, the shopkeeper will earn a profit percentage of 30%, if he does not offer any discount.
Therefore, since this value is not among the options, option E is the correct answer.

Note: The possible mistakes that the students make while solving this question is that they take 17,940 as the cost price of the TV while doing the calculations to find the profit percentage. Rs. 17,940 is the selling price of the TV and the cost price is as calculated Rs. 15,000. We should be careful while doing these steps to avoid incorrect answers.