She sold 42 oranges with profit 20%
Step-by-step explanation:
The woman sells 90 oranges by RS.160
This price with discount of 20%
We need to find how many oranges she sell by Rs.112 with profit of 20%
Assume that cost price of an orange is x
∵ She sells 90 oranges with Rs.160
- Find the selling price of 1 orange by dividing 160 by 90
∴ The selling price of an orange = [tex]\frac{160}{90}=\frac{16}{9}[/tex]
∵ She sold them with discount 20%
∵ The cost price of an orange is x
- Find the 20% of x
∵ Discount = 20% × x = [tex]\frac{20}{100}[/tex] × x = 0.2x
- To find the selling price subtract 0.2x from x
∴ The selling price = x - 0.2x
∴ The selling price of an orange = 0.8x
- Equate 0.8x by [tex]\frac{16}{9}[/tex] to find x
∵ 0.8x = [tex]\frac{16}{9}[/tex]
- Divide both sides by 0.8
∴ x = [tex]\frac{20}{9}[/tex]
Assume that the number of oranges is y
∵ She sell y oranges for Rs.112 with profit 20%
∵ The cost price of an orange is [tex]\frac{20}{9}[/tex]
- Find 20% of [tex]\frac{20}{9}[/tex]
∵ Profit = 20% × [tex]\frac{20}{9}[/tex] = [tex]\frac{20}{100}.\frac{20}{9}=\frac{4}{9}[/tex]
- Add [tex]\frac{4}{9}[/tex] to cost price to find the selling price
∴ The selling price of an orange = [tex]\frac{20}{9}[/tex] + [tex]\frac{4}{9}[/tex]
∴ The selling price of an orange = [tex]\frac{24}{9}[/tex]
- To find y divide 112 by selling price of an orange
∵ y = 112 ÷ [tex]\frac{24}{9}[/tex]
∴ y = 42
She sold 42 oranges with profit 20%
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