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If the cost price of 8 pens = Selling price of 6 pens. Find the percentage profit.

Last updated date: 20th Jun 2024
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Hint: To solve this question, we will find the cost price of each pen and selling price of each pen. Then, we will find the profit percentage by using profit percentage formula that is $=\dfrac{\text{S}\text{.P - C}\text{.P}}{\text{cost of 1 pen}}\text{ }\!\!\times\!\!\text{ 100}$, as condition of profit is $S.P > C.P$.

Complete step by step answer:
Before we start solving this problem, let us see what is Selling Price, cost price and what are conditions of profit and loss.
Selling Price is the amount a buyer pays for a product or service.
Cost price is the actual price of the product or service.
Profit is when you make money by selling a product more than its actual price that is if S.P is greater than C.P, then seller is in profit.
Loss is when you lose money by selling a product less than it’s actual price that is S.P is lesser than C.P, then seller is in loss.
Now, in question it is asked to find the profit percentage if cost of 8 pens is equals to selling price of 6 pens.
So, let cost of 1 pen be equals to x.
Then, cost of 8 pens will be equals to 8x.
Now, selling price of 6 pens = 8x as in question it is given that cost price of 8 pens = Selling price of 6 pens.
So, selling price of 1 pen = $\dfrac{8x}{6}=\dfrac{4x}{3}$
Now, profit percentage $=\dfrac{\text{S}\text{.P - C}\text{.P}}{\text{cost of 1 pen}}\text{ }\!\!\times\!\!\text{ 100}$ , S.P – C.P because it is given that there is profit and condition of profit is $S.P>C.P$
Substituting values, we get
profit percentage $=\dfrac{\dfrac{4x}{3}\text{ - x}}{x}\text{ }\!\!\times\!\!\text{ 100}$
$=\dfrac{4x-3x}{3x}\text{ }\!\!\times\!\!\text{ 100}$
= 33.33 %

So, the correct answer is 33%.

Note: While finding profit or loss in any question, always find the price of unit item as this will definitely give you hint or an idea to solve question further also, always remember the conditions that if $S.P < C.P$, then this represents loss and if $S.P > C.P$ , then this represents profit.