Question

If the cost price of 48 articles is equal to the selling price of 32 articles, then what is the profit percent?
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Answer 1

Profit and Loss

When the selling price and the cost price of a product is given, the profit can be calculated using the following formula:

$Profit = S.P - C.P$

When profit and cost price are given to us, the profit percentage can be calculated using the following formula:

$Profilt \: \% = \dfrac{Profit}{C.P} \times 100$

where S.P is the spelling price and C.P is the cost price.

Evaluation:

Let us assume that the cost price be Rs. $x$ and selling price be Rs. $y$.

As it is given that, the cost price of 48 articles is equal to the selling price of 32 articles. Therefore,

$\implies 48x = 32y$

$\implies x = \dfrac{32y}{48}$

$\implies x = \dfrac{2y}{3}$

We know that,

$\longrightarrow Profit = S.P - C.P$

By substituting the known values in formula, we obtain:

$\implies Profit = y - x$

$\implies Profit = y - \dfrac{2y}{3}$

$\implies Profit = \dfrac{y}{3}$

We know that,

$\longrightarrow Profit \: \% = \dfrac{Profit}{C.P} \times 100$

Now we have all the values which will help to find the profit percentage. By substituting the known values in the form, we get the following results:

$\implies Profit \: \% = \dfrac{\frac{y}{3}}{\frac{2y}{3}} \times 100$

$\implies Profit \: \% = \dfrac{ y}{\not3} \times \dfrac{\not3}{2 y} \times 100$

$\implies Profit \: \% = \dfrac{100}{2}$

$\implies \boxed{\rm{Profit \: \% = 50}}$

Therefore, the profit percent is 50%.

Answer 2

Given:-

• $\tt \: cost \: price \: of \: 48 \: articles \: is \\ \tt equal \: to \: the \: selling \: price \: of \\ \tt 32 \: articles.$

To Find:-

• $\tt \: profit \: percent.$

Formula using:-

$\boxed {\boxed{ \red{ \bf \: profit\% = \frac{profit}{cost \: price} \times 100}}}$

Solution:-

Profit on articles = 48 - 32 = 16

$\boxed{ \bf profit\% = \frac{16}{32} \times 100}$

$\boxed{ \bf{ \: profit\% = \frac{1}{2} \times 100}}$

$\boxed{ \bf \green{profit\% =50\ }}$