High School

Qto. 4

a) A grocer purchased 80 kg of rice at [tex]$R_s$[/tex] per kg and sold it at Rs 99 per kg.

i) Find his profit.

ii) Find his profit percent.

Answer :

Let's solve the problem step-by-step:

a) A grocer purchased 80 kg of rice at [tex]\( Rs_x \)[/tex] per kg and sold it at Rs 99 per kg.

i) Finding the Profit:

To find the profit, we will first calculate the total cost price and the total selling price.

- Total Cost Price (CP): This is the cost of buying 80 kg of rice.
[tex]\[
\text{Total Cost Price} = 80 \times Rs_x = 80 \times Rs_x
\][/tex]

- Total Selling Price (SP): This is the price at which 80 kg of rice was sold.
[tex]\[
\text{Total Selling Price} = 80 \times 99 = 7920 \text{ Rs}
\][/tex]

- Profit: This is the difference between the total selling price and the total cost price.
[tex]\[
\text{Profit} = \text{Total Selling Price} - \text{Total Cost Price}
\][/tex]
[tex]\[
\text{Profit} = 7920 - 80 \times Rs_x
\][/tex]

ii) Finding the Profit Percent:

The profit percent is calculated by dividing the profit by the total cost price and multiplying by 100.
[tex]\[
\text{Profit Percent} = \left( \frac{\text{Profit}}{\text{Total Cost Price}} \right) \times 100
\][/tex]
Substitute the expression for profit:
[tex]\[
\text{Profit Percent} = \left( \frac{7920 - 80 \times Rs_x}{80 \times Rs_x} \right) \times 100
\][/tex]
Simplify:
[tex]\[
\text{Profit Percent} = \frac{5 \times (7920 - 80 \times Rs_x)}{4 \times Rs_x}
\][/tex]

This gives us the expressions for the total profit and the profit percent.

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