In this section, you will learn how to solve profit and loss word problems.

Before look at the word problems profit and loss, if you would like to learn the shortcuts on profit and loss,

**Problem 1 :**

Cindy bought 50 pens for $100. She then sold each pen for $2.50. Find the profit or loss percentage.

**Solution :**

Cost price of 50 pens = $100

Cost price of 1 pen = 100/50 = $2

Selling price of 1 pen = $2.50

Because the selling price of 1 pen is more than cost price of 1 pen, there is profit.

**Finding Profit :**

Profit = Selling price - Cost price

Profit = 2.50 - 2

Profit = 0.50

**Finding Profit Percentage :**

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

Profit % = (0.50/2) ⋅ 100 %

Profit % = 25 %

**Problem 2 :**

Jacob purchased a house for $49,000. He spent $6000 for repair and $5,000 for air-conditioning. If he had sold the house $58,000, find the gain or loss percentage in this transaction. (If it is needed, round your answer to the nearest hundredths)

**Solution :**

Total amount spent on the house is

= 49,000 + 6,000 + 5,000

= 60,000

This is the cost price of the house ($60,000).

Selling price of the house = $58,000

Because the selling price of the house is less than the cost price, there is loss.

**Finding Loss :**

Loss = Cost price - Selling price

Loss = 60,000 - 58,000

Loss = 2,000

**Finding Loss Percentage :**

Loss % = (Loss/Cost price) ⋅ 100 %

Loss % = (2000/60000) ⋅ 100 %

Loss % = 3.33 %

**Problem 3 :**

Goods are purchased for $1500. If one fifth of the goods sold at a profit of 5% and the remaining four-fifth of the goods at a profit of 10%, find the net profit percentage.

**Solution :**

Cost price of one-fifth of the goods is

= 1/5 ⋅ 1500

= 300

Selling price of one-fifth of the goods (at 5% profit) is

= (100 + 5)% of 300

= 105% of 300

= 1.05 ⋅ 300

= 315

Cost price of remaining four-fifth of the goods is

= 4/5 ⋅ 1500

= 1,200

Selling price of the remaining four-fifth of the goods (at 10% profit) is

= (100 + 10)% of 1200

= 110% of 1200

= 1.10 ⋅ 1200

= 1,320

Selling price of the total goods

= 315 + 1,320

= 1,635

**Finding Net Profit :**

Net profit = S.P of total goods - C.P of total goods

Net Profit = 1635 - 1500

Net Profit = 135

**Finding Net Profit Percentage :**

Net profit % = (Net profit/Cost price) ⋅ 100 %

Net profit % = (135/1500) ⋅ 100 %

Net profit % = 9 %

**Problem 4 :**

A trader bought a product for $200. If marks his goods 20% above the cost price and gives a discount of 10% for cash, find his profit percentage

**Solution :**

Cost price of the product = $100

Marked price (20% above the cost price) is

= (100 + 20) % of 200

= 120% of 200

= 1.2 ⋅ 200

= 240

Selling price price is the price which is after 20% discount from the marked price.

So, the selling price is

= (100 - 10) % of Marked price

= 90% of 240

= 0.9 ⋅ 240

= 216

**Finding Profit :**

Profit = Selling price - Cost price

Profit = 216 - 200

Profit = 16

**Finding Profit Percentage :**

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

Profit % = (16/200) ⋅ 100 %

Profit % = 8 %

**Problem 5 :**

A person wants to get 20% profit after selling his object at 20% discount. Find the required percentage increase in marked price.

**Solution :**

Let the cost price be $100.

Then, the selling price (at 20% profit) is

= (100 + 20)% of 100

= 120% of 100

= 1.2 ⋅ 100

= 120

Selling price is the price which is after 20% discount from the marked price.

It has been illustrated in the picture given below.

From the above picture, we get

Selling price = (100 - 20)% of Mmarked price

120 = 80% of x

120 = 0.8 ⋅ x

Divide both sides by 0.8

120/0.8 = x

1200/8 = x

150 = x

So, the marked price is $150.

Here,

Cost price = $100

Marked Price = $150

Hence, the required percentage increase is 50%

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