Question

A shopkeeper sells 25 articles at Rs 45 per article after giving 10% discount and earns 50% profit. If the discount is not given, find the profit gained in percentage.

Answer 1

Hint: First calculate the marked price MP of an article if the discount percentage D is 10% using the relation \[D=\left( \dfrac{MP-SP}{MP} \right)\times 100\] and after that calculate the cost price of an article if the shopkeeper earns 50% profit. Then calculate the profit obtained for each article and calculate the new profit gained in percentage.

Complete step-by-step answer:
We know the formula for selling price (SP) and discount percentage (D) in terms of marked price (MP) is given as,
\[D=\left( \dfrac{MP-SP}{MP} \right)\times 100\]
It is said that the selling price (SP) of one article is 45 rupees.
Applying the above formula for discount percentage D by substituting values of marked price MP and selling price SP,
\[10=\left( \dfrac{MP-45}{MP} \right)\times 100\]
On dividing both sides with 100 we get,
\[\dfrac{10}{100}=\left( \dfrac{MP-45}{MP} \right)\]
By cross multiplying the terms we get,
\[10MP=\left( MP-45 \right)100\]
Simplifying the above expression we get,
$10MP = 100MP – 4500$
$90MP = 4500$
Dividing both sides with 90 we get,
\[MP=\dfrac{4500}{90}\]
Dividing 4500 with 90 we get the marked price MP in rupees as,
$MP = 50$
It is said that the shopkeeper earns a profit percentage (P) as 50%.
We know the formula for cost price CP in terms of selling price SP and profit percentage P is given as,
\[CP=\dfrac{SP\cdot 100}{100+P}\]
Applying the above formula and substituting the values of profit percentage and selling price to find the cost price,
\[CP=\dfrac{45\cdot 100}{100+50}\]
Multiplying 45 with 100 and simplifying we get,
\[CP=\dfrac{4500}{150}\]
On dividing 4500 with 150 we get cost price CP in rupees as,
\[CP = 30\]
We know the formula for profit PF is given as \[PF = SP – CP\],
Applying the above formula we get,
\[PF = 50 – 30\]
\[PF = 20\]
The profit percentage P in terms of profit and CP is given as,
\[P=\dfrac{PF}{CP}\times 100\]
This implies the required profit percentage P becomes,
\[P=\dfrac{20}{30}\times 100\]
\[\begin{align}
  & P=\dfrac{200}{3}\% \\
 & =66.6\%
\end{align}\]
Hence, the profit gained in percentage is \[66.6\%\].

Note: Calculate the marked price carefully and formulas should be applied properly. After calculating the cost price CP calculates a new profit percentage gained in the same case to obtain the final answer. Here, According to the question, when discount is not given then marked price becomes selling price that’s why we have taken 50 as selling price.