# 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?

Answer

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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.

Complete step-by-step answer:

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 \[100%\].

Complete step-by-step answer:

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 \[100%\].

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