Question

The juice stall at the circus stocked just 2 brands of orange juice tetra packs; Brand A costs 1.00 per pack Brand B costs 1.50 per pack. Last week, Brand A contributed to \[m\% \] of the stall’s revenue, and accounted for \[n\% \] of the sales of juice tetra packs. Which of the following expresses \[m\] in terms of \[n\]?
A.\[\dfrac{{100n}}{{150 - n}}\]
B.\[\dfrac{{200n}}{{250 - n}}\]
C.\[\dfrac{{200n}}{{300 - n}}\]
D.\[\dfrac{{250n}}{{400 - n}}\]
E.\[\dfrac{{300n}}{{500 - n}}\]

Answer 1

Hint: Here we need to express \[m\] in terms of \[n\]. We will find the revenue generated by Brand A and Brand B which will be equal to the product of number of units sold and cost per unit. Then we will find the total revenue which will be equal to the sum of revenue generated by Brand A and revenue generated by Brand B. We will then equate the revenue generated by Brand A with \[m\% \] of the total revenue. From there we will get the expression of \[m\] in terms of \[n\].

Complete step-by-step answer:
Let the total number of units of orange juice sold be 100.
According to question, number of units sold by Brand A is \[n\] and number of units sold by Brand B is \[100 - n\].
Revenue generated by Brand A \[ = \]number of units of Brand A sold \[ \times \] cost per unit
Substituting the values, we get
Revenue generated by Brand A \[ = n \times 1\]
Revenue generated by Brand B \[ = \]number of units of Brand A sold \[ \times \] cost per unit
Therefore,
Revenue generated by Brand B \[ = \left( {100 - n} \right) \times 1.5\]
Total revenue generated \[ = \] Revenue generated by Brand A \[ + \] Revenue generated by Brand B
Substituting the values of revenue generated by Brand A and Revenue generated by Brand B, we get
Total revenue generated \[ = n \times 1 + \left( {100 - n} \right) \times 1.5{\rm{ }}\]
Simplifying the terms, we get
Total revenue generated \[ = 150 - 0.5n\]……………….\[\left( 1 \right)\]
According to question, revenue generated by Brand A is equal to m% of the total revenue generated
Therefore,
Revenue generated by Brand A \[ = m\% \] of total revenue
Substituting the value of revenue generated by Brand A and total revenue obtained in equation \[\left( 1 \right)\], we get
$\Rightarrow$ \[n = \dfrac{m}{{100}}\left( {150 - 0.5n} \right)\]
Multiplying 100 on both sides, we get
$\Rightarrow$ \[100n = m\left( {150 - 0.5n} \right)\]
Dividing \[\left( {150 - 0.5n} \right)\] on both sides, we get
$\Rightarrow$ \[\dfrac{{100n}}{{150 - 0.5n}} = m\]
Simplifying the expression, we get
$\Rightarrow$ \[\dfrac{{100n}}{{150 - \dfrac{1}{2}n}} = m\]
$\Rightarrow$ \[m = \dfrac{{200n}}{{300 - n}}\]
Hence, the correct answer is option C.

Note: We have used revenue generated by both the brands here for getting the required expression. Revenue is defined as the money earned from the business operations. It is also called sales as it is the income generated from the normal business operation. The sales revenue is equal to the product of sales price and the number of units sold.