**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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