**Solved Problems on Profit and Loss :**

In this section, we will see how to solve problems with the concept of profit and loss.

Profit (or) gain = Selling price - Cost price

Loss = Cost price - Selling price

Profit % = (Profit / Cost price) ⋅ 100

Loss % = (Loss / Cost price) ⋅ 100

Cost price = [100 / (100 - loss%)] ⋅ Selling price

Cost price = [100 / (100 + profit%)] ⋅ Selling price

Selling price = [(100 + profit%)/100] ⋅ Cost price

Selling price = [(100 - loss%)/100] ⋅ Cost price

**Example 1 :**

The product is marked at 20% above the cost price. It is then sold at 90% of the selling price. The profit is $120. What is the cost price of this product.

**Solution :**

Let x be the the cost price.

120% of x = Marked price

Selling price = 90% of marked price

= 90% of (120% of x)

= 0.90(1.2x)

= 1.08x

Profit = $120 ---(1)

Profit = Cost price - Selling price

= x - 1.08x

= x(1 - 1.08)

Profit = 0.08x ---(2)

(1) = (2)

0.08x = 120

x = 120/0.08

x = 1500

Hence the cost price is 1500.

**Example 2 :**

A shop purchased some shoes at $65 per pair. It then sold them at $74 per pair. The shopkeeper calculated that the profit earned was $440 when there were 5 pairs of shoes left. How many pairs of shoes did the shop purchase initially ?

**Solution : **

Let x be the number of pair of shoes in the shop.

Pair of shoes left = 5

Cost price of pair of shoes going to be sold = 65x

Selling price of pair of shoes has been sold = 74(x - 5)

Profit = 440

Profit = Selling price - Cost price

74(x - 5) - 65x = 440

74x - 370 - 65x = 440

9x = 440 + 370

9x = 810

x = 810/9

x = 90

So, the shop purchased 90 pairs of shoes initially.

**Example 3 :**

The selling price of a sofa set is $12000. It is later sold at $6500 at an exhibition. The profit made is 30%. What is the percentage of profit if the profit is $5000 ?

**Solution :**

Selling price of a sofa = 12000

By selling the sofa at the cost of $6500, it made a profit 30%.

Let x be the cost price of sofa.

130% of x = 6500

1.30x = 6500

x = 6500/1.30

x = 5000

Cost price of sofa is 5000.

Profit % = (Profit / cost price) ⋅ 100

= (5000/5000) ⋅ 100

= 100%

After having gone through the stuff given above, we hope that the students would have practiced problems in profit and loss.

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