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# Rajendra and Rehana own a business. Rehana receives $25%$ of the profit in each month. If Rehana received $Rs.2080$ in a particular month, what is the total profit in that month?

Last updated date: 21st Sep 2024
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Hint: Use the formula of percentage which says that $x%$ of $y$ has the value $\dfrac{xy}{100}$, to calculate the total profit earned by them in a month. We can also use a unitary method to calculate the total profit earned.
We know that Rehana receives $25%$ of total profit in each month. For a particular month, she received $Rs.2080$. We have to calculate the total profit earned by them in that month.
Let’s assume that the total profit earned by them in that particular month is $Rs.a$.
$25%$ of $Rs.a$ is $Rs.2080$.
We know that the value of $x%$ of $y$ is $\dfrac{xy}{100}$.
Substituting $x=25,y=Rs.a$, we have $25%$ of $Rs.a=\dfrac{25\left( a \right)}{100}=Rs.2080$.
Simplifying the above equation, we have $\dfrac{a}{4}=Rs.2080$.
$\Rightarrow a=Rs.2080\times 4=Rs.8320$
Thus, we have $a=Rs.8320$.
Hence, the total profit earned by them in that particular month is $Rs.8320$.
Note: We can also solve this question using a unitary method. If $Rs.a$ denotes the total profit earned in a month, then $Rs.a$ is equivalent to $100%$ of profit. As $25%$ of total profit is $Rs.2080$, $1%$ of total profit will be $\dfrac{Rs.2080}{25}$. Thus, $100%$ of total profit will be $\dfrac{Rs.2080}{25}\times 100$, which is equal to $Rs.8320$. Unitary method is a technique used for solving a problem by first finding the value of a single unit and then finding the necessary value by multiplying the single unit value. The word unitary refers to a single or individual unit. Hence, this method aims at determining the value in relation to a single unit. Percentage is a number or a ratio that represents a fraction out of $100$. It is a dimensionless number. As percentage represents a fraction out of $100$, we can take the total value of quantity as $100%$.