## 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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