**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%

To learn profit and loss shortcuts,

Apart from the stuff given in this section, if you need any other stuff in math, please use our google custom search here.

HTML Comment Box is loading comments...

You can also visit the following web pages on different stuff in math.

**WORD PROBLEMS**

**Word problems on simple equations **

**Word problems on linear equations **

**Word problems on quadratic equations**

**Area and perimeter word problems**

**Word problems on direct variation and inverse variation **

**Word problems on comparing rates**

**Converting customary units word problems **

**Converting metric units word problems**

**Word problems on simple interest**

**Word problems on compound interest**

**Word problems on types of angles **

**Complementary and supplementary angles word problems**

**Trigonometry word problems**

**Markup and markdown word problems **

**Word problems on mixed fractrions**

**One step equation word problems**

**Linear inequalities word problems**

**Ratio and proportion word problems**

**Word problems on sets and venn diagrams**

**Pythagorean theorem word problems**

**Percent of a number word problems**

**Word problems on constant speed**

**Word problems on average speed **

**Word problems on sum of the angles of a triangle is 180 degree**

**OTHER TOPICS **

**Time, speed and distance shortcuts**

**Ratio and proportion shortcuts**

**Domain and range of rational functions**

**Domain and range of rational functions with holes**

**Graphing rational functions with holes**

**Converting repeating decimals in to fractions**

**Decimal representation of rational numbers**

**Finding square root using long division**

**L.C.M method to solve time and work problems**

**Translating the word problems in to algebraic expressions**

**Remainder when 2 power 256 is divided by 17**

**Remainder when 17 power 23 is divided by 16**

**Sum of all three digit numbers divisible by 6**

**Sum of all three digit numbers divisible by 7**

**Sum of all three digit numbers divisible by 8**

**Sum of all three digit numbers formed using 1, 3, 4**

**Sum of all three four digit numbers formed with non zero digits**