To calculate percentage change, we use the formula given below.
If Old value > New value, then decrease will happen. We may find percentage decrease.
If Old value < New value, then increase will happen. We may find percentage increase.
Percentage change
= (|Old value - New value| / Old value) x 100%
Problem 1 :
In a sale the price of a sofa is reduced from $2500 to $1840 what is the percentage decrease?
Solution :
The price of a sofa is reduced from $2500 to $1840.
Reduction amount = |2500 - 1840|
= 660
Percentage decrease = (660/2500) × 100%
= 26.4%
Problem 2 :
The population of Northern Ireland in 1911 was 1,256,561 in 2011 the population was 1,810, 863.
Solution :
Population in 1911 = 1256561
Population in 2011 = 1810863
Difference = |1810863 - 1256561|
= 554302
Percentage increase= (554302/1256561) × 100%
= 44.1%
Problem 3 :
In 2000 the price of a house was $72,600. By 2010 the price of the house had increased to $ 125,598. Find the percentage increase in the price of the house from 2000 to 2010.
Solution :
2000 the price of a house = $72,600
2010 the price of a house = $125598
Difference = |125598 - 72600|
= 52998
Percentage increase= (52998/72600) × 100%
= 73%
Problem 4 :
A website had 140,000 views in March. It had 198,800 views in April. Work out the percentage increase in views.
Solution :
Views in March = 140000
Views in April = 198800
Difference = |198800 - 140000|
= 58800
Percentage increase = (58800/140000) × 100%
= 42%
So, 42% Percentage increase in views.
Problem 5 :
In a sale the price of microwave decreases from $50 to $39. Work out the percentage decrease in price.
Solution :
The price of microwave decreases from $50 to $39.
Decrease amount = |50 – 39|
= 11
Difference = (11/50) × 100%
= 22%
So, the percentage decrease in price = 22%.
Problem 6 :
An empty bucket weight 800 g. The weight of the bucket increases to 2.1 kg when filled with water.
Calculate the percentage increase in the weight of the bucket. Give your answer to two significant figures.
Solution :
Weight of empty bucket = 800 g
Converting into kg.
= 0.8 kg
When it was with water = 2.1 kg
= |2.1 - 0.8|
= 1.3
The percentage increase in the weight of the bucket
= (1.3/0.8) × 100%
= 1.625%
Problem 7 :
Orla weighed 3.77 kg when she was born. On Orla’s second birthday she weighed 12.8 kg. Calculate the percentage increase in her weight.
Solution :
Weight of her = 3.77 kg
Weight of her on second birthday = 12.8 kg
Difference in weight = |3.77 - 12.8|
= 9.03
Percentage increase = (9.03/3.77) × 100%
= 239.52%
So, the percentage increase in her weight is 239.52%
Problem 8 :
Rebecca and Jennifer take part in a training camp to improve their performance at the javelin.
The table below shows Rebecca’s and Jennifer’s best javelin throw before and after the training camp.
Which athlete had the biggest percentage improvement?
You must show your method.
Solution :
Rebecca :
Before training camp = 50.02m
After training camp = 51.27m
Training camp = |50.02 – 51.27|
= 1.25
Percentage increase = (1.25/50.02) × 100%
= 2.499%
Jennifer :
Before training camp = 45.88m
After training camp = 46.92m
Training camp = |45.88 – 46.92|
= 1.04
Percentage increase = (1.04/45.88) × 100%
= 2.2668%
So, Rebecca has improved.
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