Question

A man buys goods at 25% of the list price. He desires to mark the goods so that he can give a discount of 20% on the marked price and still clear a profit of 25% on the selling price. What percent of the list price must he mark the goods?
(a) 125%
(b) 100%
(c) 80%
(d) 75%

Answer 1

Hint: First find the CP which is 25% of list price. Take X as the listed price. The SP will be the sum of CP and profit. Thus find an expression for SP. Now the marked price is the sum of SP and discount. Take MP as Y. Hence marked % on list price is Y by X.

Complete step-by-step answer:
It is said that a man buys goods at 25% off the list price. Let us assume that the list price be rupees X.
Thus the cost price is 25% of the list price. So, we can write
Cost price = 25% off list price.
Cost price = X – 25% of X = \[X-\dfrac{25}{100}X=X-\dfrac{X}{4}=\dfrac{3X}{4}\].
\[\therefore \] Cost price (CP) = \[\dfrac{3X}{4}\] ----------- (1)
He gives a discount of 20% on the marked price (MP) and get a profit of 25% on the selling price (SP).
\[\therefore \] Profit = 25% on the selling price.
We know that profit = selling price – cost price = SP – CP
\[\therefore \] SP = CP + profit
We have been given that profit is 25% of SP.
\[\therefore \]SP = CP + 25% of SP \[\left\{ \because CP=\dfrac{3X}{4} \right\}\]
\[\begin{align}
  & SP=\dfrac{3X}{4}+\dfrac{25}{100}\times SP \\
 & SP-\dfrac{SP}{4}=\dfrac{3X}{4} \\
 & \dfrac{3SP}{4}=\dfrac{3X}{4} \\
\end{align}\]
\[\Rightarrow SP=X\] ---------------------- (2)
Thus the selling price is the listed price of the product.
We have been given a discount of 20% of the Marked price. Let us assume the marked price as ‘Y’. We know that formula,
Marked price = Selling price + Discount
\[\therefore \] MP = SP + discount
\[\therefore \] SP = MP – discount
SP = MP – 20% of MP
Put SP = X and MP = Y in the above expression.
\[\begin{align}
  & X=Y-\dfrac{20}{100}\times Y \\
 & X=Y-\dfrac{Y}{5}=\dfrac{4Y}{5} \\
\end{align}\]
\[\therefore X=\dfrac{4Y}{5}\Rightarrow Y=\dfrac{5X}{4}\] ---------------- (3)
Hence the marked percentage on the list price,
= (Marked price / listed price) \[\times \] 100
\[\begin{align}
  & =\dfrac{Y}{X}\times 100=\dfrac{\dfrac{5X}{4}}{X}\times 100 \\
 & =\dfrac{5}{4}\times 100=\dfrac{500}{4}=125\% \\
\end{align}\]
Thus we got the marked percentage of the list price as 125%.
\[\therefore \] Option (a) is the correct answer.

Note: The key important points to keep in mind are the formulas of Profit, SP, CP, MP and discount. Thus remember the formula connecting all these and hence the solution becomes easy to solve. Some students consider the list price and the cost price as the same and then proceed with the solution by assuming the cost price as x+20% of x. But, this is not true and students must refrain from making this mistake.