The selling price of 12 eggs is equal to the cost price of 16 eggs find the profit percent

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Given:

Selling price of 12 eggs is equal to the cost price of 15 eggs.

To do:

Here, we have to find the gain percentage.

Solution:

Let the cost price of 15 eggs be $a$.

So,

Selling price of 12 eggs $=a$

Selling price of 1 egg $=\frac{a}{12}$

Selling price of 15 eggs $=\frac{15a}{12}$

Now,

Profit $=$ SP of 15 eggs $-$ CP of 15 eggs

Profit$=\frac{15a}{12}-a$

Profit$=\frac{15a-12a}{12}$

Profit$=\frac{3a}{12}$

Profit$=\frac{a}{4}$

Therefore, profit % is as below,

Profit %$=\frac{Profit}{CP}\times100\%$

Profit%$=\frac{\frac{a}{4}}{a}\times100\%$

Profit%$=\frac{1}{4}\times100\%$

$\mathbf{Profit\ \%\ =\ 25\ \%}$

So, the answer is 25%.

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Updated on 10-Oct-2022 10:29:35

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The sold price of $12$ eggs is equal to the cost price of $16$ eggs. Find the profit percentage.

Answer

Verified

Hint:We will first see that the sold price is more than the cost price of the eggs and therefore we will incur a profit percentage. We will first put the statements given the question into a mathematical form. Once we have done that we will then simply find the ratio of the sold price and cost price. This ratio will ultimately help in finding the profit percentage. Once we get the values of both the selling price and the cost price we will find the profit and then divide the calculated profit and divide it by the cost price, and then find the percentage of the profit.

Complete step by step answer:
The sold price of $12$ eggs is equal to the cost price of $16$ eggs. So we write as,
$S.P \times 12 = C.P \times 16$
The above expression is the form of the given statement.
Now we find the ratio as,
$\dfrac{{S.P.}}{{C.P.}} = \dfrac{{16}}{{12}}$
The ratio is ,
$\dfrac{{S.P.}}{{C.P.}} = \dfrac{4}{3}$,
Which means when the selling price is $4$the cost price is $3$, the profit will be $1$.To find the profit percentage,
$P\% = \dfrac{P}{{C.P.}} \times 100$,
Which gives us,
$P\% = \dfrac{1}{3} \times 100$
The answer will be,
$\therefore P\% = 33.33\% $

Hence, the profit percent is $33.33\% $.

Note:The profit percent of a transaction is said to be as the profit earned per $100$ of the unit or the good which is sold. So say we earn ${\text{10}}$ for a transaction of ${\text{100}}$, our profit percentage would be $10\% $, Also remember the profit percent is always calculated on the cost price not on the selling price.

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