SOLVING PROBLEMS INVOLVING COST PRICE AND SELLING PRICE ARE EQUAL
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.
Solving Problems Involving Cost Price and Selling Price are Equal - Examples
Example 1 :
The cost price of 21 articles is equal to selling price of 18 articles. Find the gain or loss percent.
Solution :
If cost price of 21 articles is equal to selling price 21 articles, then we say that there is no profit or loss.
Given is,
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.
Solution :
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
= 50%
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
= 10%
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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