Solving Problems Involving Cost Price and Selling Price are Equal :
In this section, we will see how to solve problems involving the condition cost price and selling price are equal.
Example 1 :
The cost price of 21 articles is equal to selling price of 18 articles. Find the gain or loss percent.
If cost price of 21 articles is equal to selling price 21 articles, then we say that there is no profit or loss.
Cost price of 21 articles = Selling price of 18 articles.
Cost of 3 articles can be considered as profit.
Profit % = (Profit / Cost price) ⋅ 100
Profit % = (3/18) ⋅ 100
profit % = 16.66
Example 2 :
By selling 33 meters of cloth, one gains the selling price of 11 meters. Find the gain percent.
Since he had profit, the selling price might be greater.
Profit = Selling price - Cost price
Profit = Selling price of 33 m cloth - Cost price of 33m cloth
Given profit is selling price of 11 meters of cloth.
Selling price of 11 m of cloth = Selling price of 33 m cloth - Cost price of 33 m cloth
Simplifying this, we get
Cost price of 33 m cloth = Selling price of 22 m cloth
Profit % = (profit / Cost price) ⋅ 100
= (Selling price of 11 m of cloth / Selling price of 22 m cloth) ⋅ 100
So, he earns 50% profit.
Example 3 :
A vendor bought bananas at 6 for $10 and sold them at 4 for $6. Find his gain or loss percent.
Cost price of 6 bananas = $10
Cost price of 1 banana = 10/6 = 5/3 ----(1)
Selling price of 4 bananas = $6
Selling price of 1 banana = 6/4 = 3/2 ----(2)
By changing the denominators of (1) and (2) as same, we get
Cost price of 1 banana = 20/12 ----(1)
Selling price of 1 banana = 18/12 ----(2)
profit% = (Profit / Cost price) ⋅ 100
= [(2/12) / (20/12)] ⋅ 100
= (2/20) ⋅ 100
Hence the profit is 10%.
After having gone through the stuff given above, we hope that the students would have learned how to solve problems involving cost price and selling price are equal.
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