**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.

**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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