Question

A trader buys goods at a 20% discount on the marked price. If he wants to make a profit of 25% after allowing a discount of 20%. By what percent should his marked price be greater than the original marked price?
(A) 15%
(B) 65%
(C) 25%
(D) 20%

Answer 1

Hint: Assume the original marked price of the good is Rs.x. Now, a 20% discount is given on the marked price. The price at which the trader buys the goods is equal to \[\left( x20\%\text{ }of\text{ }x \right)\] .
It means the cost price for the trader is \[\left( x20\%\text{ }of\text{ }x \right)\] . Calculate the price at which the trader buys the goods. Now, assume the marked price at which the good is getting sold by the trader be Rs. y. After allowing a discount of 20% on the marked price by the trader, the price at which the trader sells his goods is equal to \[\left( y20\%\text{ }of\text{ }y \right)\] . It means that the selling price for the trader is \[\left( y20\%\text{ }of\text{ }y \right)\]. It is also given that the trader makes a profit of 25%. So, The selling price of the good = Cost price of the good + 25% of the cost price of the good. Now, put the values of the cost price and the selling price of the good for the trader, and solve it further to get the value of y in terms of x. Now, subtract x from y and get the percentage with respect to x.

Complete step-by-step answer:
First of all, let us assume that the original marked price of the good is Rs. x …………………….(1)
It is given that the trader buys goods at a 20% discount on the marked price.
From equation (1), we have the original marked price of the good.
The price at which the trader buys the good = x – 20% of x = \[x-\dfrac{20}{100}x=x-\dfrac{x}{5}=\dfrac{4x}{5}\] ……………………..(2)
Let us assume that the price marked by the trader to sell his good be Rs. y ……………………….(3)
After allowing a discount of 20% on the marked price by the trader,
The price at which the trader sells his good = y – 20% of y = \[y-\dfrac{20}{100}y=y-\dfrac{y}{5}=\dfrac{4y}{5}\] ……………………..(4)
It is also given that the trader makes a profit of 25% after allowing a discount of 20%.
The trader would make a profit of 25% on the price at which he has bought.
From equation (2), we have the price at which the trader bought the good and from equation (4), we have the price at which the trader sells his good to make a profit of 25%. In other words, we can say that the selling price of the goods is 25% more than the cost price of the goods. So,
The selling price of the good = Cost price of the good + 25% of the cost price of the good ……………………(5)
The cost price of the good for the trader is the same as the price at which the trader buys the good =
\[\dfrac{4x}{5}\] …………………………………(6)
The selling price of the good for the trader is the same as the price at which the trader sells the good = \[\dfrac{4y}{5}\] …………………………………(7)
Now, from equation (5), equation (6), and equation (7), we get
\[\begin{align}
  & \Rightarrow \dfrac{4y}{5}=\dfrac{4x}{5}+25\%\,of\,\dfrac{4x}{5} \\
 & \Rightarrow \dfrac{4y}{5}=\dfrac{4x}{5}+\dfrac{25}{100}\times \dfrac{4y}{5} \\
 & \Rightarrow \dfrac{4y}{5}=\dfrac{4x}{5}+\dfrac{1}{4}\times \dfrac{4x}{5} \\
 & \Rightarrow \dfrac{4y}{5}=\dfrac{4x}{5}+\dfrac{x}{5} \\
 & \Rightarrow \dfrac{4y}{5}=\dfrac{5x}{5} \\
\end{align}\]
\[\Rightarrow y=\dfrac{5x}{4}\] ………………………………(8)
From equation (1), we have the original marked price.
The difference between the marked price of the good and the original marked price = \[\dfrac{5x}{4}-x=\dfrac{5x-4x}{4}=\dfrac{x}{4}\] …………………………….(9)
Percentage by which the marked price is greater than the original marked price = \[\dfrac{\dfrac{x}{4}}{x}\times 100=\dfrac{100}{4}\] = 25%.
Therefore, the marked price of the good must be greater than the original marked price by 25%.
Hence, option (C) is the correct one.

Note: In this question, one might get confused in the given condition “If the trader wants to make a profit of 25% after allowing a discount of 20%” because the marked price while selling the good is not given. We have already assumed the original marked price of the good as Rs. x. There is not a problem if it is not given. Just assume the marked price at which the goods are getting sold be Rs. y. Now, form the mathematical equation carefully.