Formula to find percentage increase/decrease
Problem 1 :
The price of a TV is $260. In a sale the price is decreased by 20%. Work out the price of the TV sale.
Solution :
Price of the TV = $260
It is given that the price of the TV is decreased by 20%.
Then, the selling price of the TV :
= 80% of 260
= 0.80(260)
= $208
Problem 2 :
The value of a painting rises from $120000 to $192000. Work out the percentage increase in the value of painting.
Solution :
Original price of the painting = $120000
After increase, the new price = $192000.
Price increase = 192000 - 120000
= $72000
Percentage increase :
= ⁷²⁰⁰⁰⁄₁₂₀₀₀₀ ⋅ 100%
= ⅗ ⋅ 100%
= 3 ⋅ 20%
= 60%
The value of the paiting is increased by 60%.
Problem 3 :
A puppy weighed 2 kg. Eight weeks later the puppy weighed 3.5 kg. What was the percentage increase in the Puppy's weight?
Solution :
Weight of puppy = 2 kg.
Puppy's weight after eight weeks = 3.5 kg.
Increase in weight in eight weeks :
= 3.5 - 2
= 1.5 kg.
Percentage increase :
= (1.5/2) ⋅ 100%
= 0.75 ⋅ 100%
= 75%
Puppy's weight was increased by 75%.
Problem 4 :
Peter's weight decreases from 80 kg. to 64 kg. Calculate the percentage decrease in Peter's weight.
Solution :
Old weight = 80 kg.
New weight = 64 kg.
Decrease in weight :
= 80 - 64
= 16 kg.
Percentage decrease :
= ¹⁶⁄₈₀ ⋅ 100%
= ⅕ ⋅ 100%
= 1 ⋅ 20%
= 20%
Peter has reduced 20% of his weight.
Problem 5 :
Alice buys a book for $19.80 A year later she sells the book for $12.87 Calculate the percentage decrease in the value of the book.
Solution :
Cost price of the book = $19.80
Selling price = $12.87
Decrease in the price :
= 19.80 - 12.87
= $6.93
Percentage decrease :
= (6.93/19.80) ⋅ 100%
= 35%
The value of the book is decaresed by 35%.
Problem 6 :
The volume of juice in a can is increased from 250 ml. to 330 ml. Work out the percentage increase.
Solution :
Original volume of juice in a can = 250 ml.
Volume of juice in can after increase = 330 ml.
Increase in volume :
= 330 - 250
= 80 ml.
Percentage increase :
= ⁸⁰⁄₂₅₀ ⋅ 100%
= ⁸⁄₂₅ ⋅ 100%
= 8 ⋅ 4%
= 32%
Volume of juice in can is increased by 32%.
Problem 7 :
Sarah bought a TV for $250. Three years later she sold it for $180. Work out her percentage loss.
Solution :
Cost price of the TV = $250
Selling price = $180
Cost price > Selling price ----> Loss
Loss = Cost price - Selling price
= 250 - 180
= $70
Percentage loss :
= ⁷⁰⁄₂₅₀ ⋅ 100%
= ⁷⁄₂₅ ⋅ 100%
= 7 ⋅ 4%
= 28%
Problem 8 :
A car is travelling at 40 kilometers per hour. The car increases its speed to 56 kilometers per hour. Calculate the percentage increase in the speed of the car.
Solution :
Initial speed of car = 40 km. per hour
Increased speed = 56 km. per hour
Increase in speed :
= 56 - 40
= 16 km. per hour
Percentage increase in speed of the car :
= ¹⁶⁄₄₀ ⋅ 100%
= ⅖ ⋅ 100%
= 2 ⋅ 20%
= 40%
Problem 9 :
Susan buys an antique for $120 and sells it for $216. Work out her percentage profit.
Solution :
Cost price of an item = $120
Selling price of an item = $216
Selling price > Cost price ----> Profit
Profit = Sleeing price - Cost price
= 216 - 120
= $96
Percentage profit :
= ⁹⁶⁄₁₂₀ ⋅ 100%
= ⅘ ⋅ 100%
= 4 ⋅ 20%
= 80%
Problem 10 :
Holly bought a table for $80 She sold the table for $108 Find the percentage profit
Solution :
Cost price = $80
Selling price = $108
Selling price > Cost price ----> Profit
Profit = Selling price - Cost price
= 108 - 80
= 28
Percentage profit :
= ²⁸⁄₈₀ ⋅ 100%
= ⁷⁄₂₀ ⋅ 100%
= 7 ⋅ 5%
= 35%
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