**Profit and Loss Problems : **

In this section, we are going to learn, how to solve problems on profit and loss step by step.

Before we look at the problems, if you want to know the shortcuts required for solving problems on profit and loss ,

**Problem 1 :**

John bought a car for $18000 and sold it to his friend for $18900. Find the profit percentage.

**Solution :**

Profit = Selling price - Cost price.P

Profit = 18900 - 18000

Profit = 900

Profit % = (Profit/Cost price) ⋅ 100 %

Profit % = (900/18000) ⋅ 100 %

Profit % = 5 %

**Problem 2 :**

Peter bought an item at $300 and sold it for $240. Find the loss percentage.

**Solution :**

Loss = Cost price - Selling price

Profit = 300 - 240

Profit = 60

Loss % = (Loss/Cost price) ⋅ 100 %

Loss % = (60/300) ⋅ 100 %

Loss % = 20 %

**Problem 3 :**

A sold a laptop to B at 15% profit. B sold the same laptop to C at 20% profit. If C had paid $1656 for it, find the price at which A bought the laptop.

**Solution : **

Let "x" be the price at which A bought the laptop.

Cost price of B = 115% of x

Cost price of B = 1.15x

Cost price of C = 120% of 1.15x

Cost price of C = 1.20 ⋅ 1.15x

Cost price of C = 1.20 ⋅ 1.15x

Cost price of C = 1.38x

It is given that C paid $1656. So we have

1.38x = 1656

Divide both sides by 1.38

x = 1656/1.38

x = 165600/138

x = 1200

Hence, the price at which A bought the laptop is $1200.

**Problem 4 :**

Michael sold an item at a loss of 5%. If he had sold at a profit of 20%, he would have got $100 more. Find the cost is the cost price of the item.

**Solution :**

Let "x" be the cost price of the chair

S.P (-5%) = 95% of x

= 0.95x --------(1)

S.P (+10%) = 120% of x

= 1.2x ---------(2)

In (2), he got $100 more than (1). So we have

(2) - (1) = 100

1.2x - 0.95x = 100

0.25x = 100

Divide both sides by 0.25

x = 100/0.25

x = 10000/25

x = 400

Hence, the cost price of the item is $400.

**Problem 5 :**

A man bought 20 units of a product at the cost of $400 and sold 5 units at the cost of $125. Find the profit or loss percentage.

**Solution :**

Cost price for 20 units = $400

Cost price for one unit = 400/20 = $20

Selling price for 5 units = $125

Selling price for one unit = 125/5 = $25

Because selling price is more than cost price, there is profit.

Profit = Selling price - Cost price

Profit = 25 - 20

Profit = 5

Profit % = (Profit/Cost price) ⋅ 100 %

Profit % = (5/20) ⋅ 100 %

Profit % = 25 %

After having gone through the stuff given above, we hope that the students would have understood "Profit and loss problems".

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