Percentage change - WJECPercentage increase and decrease
Percentages can be used to increase or decrease a quantity relative to its size. Shops reduce their goods by a percentage and the government increases the cost of goods by adding on a percentage tax.
Percentage increase and decrease - Intermediate and Higher tier
You may also need to increase a value by a given percentage. In this case, add on the percentage change. Read the question carefully so that you know whether you are increasing or decreasing the amount.
Question
zs7gk7h Cai's rent is increasing by 3.1% from 拢460 per calendar month (pcm). Elin's landlord is giving her a reduction of 3.5% on her calendar monthly rent of 拢484. What will they each be paying in rent after these changes?
Cai
拢460 梅 100 脳 3.1 = 拢14.26 increase
New rent 鈥 拢460 + 拢14.26 = 拢474.26 pcm
Elin
拢484 梅 100 脳 3.5 = 拢16.94 decrease
New rent 鈥 拢484 鈭 拢16.94 = 拢467.06 pcm
There is an alternative way of calculating the new rents.
Cai
Increase is 3.1%, so new rent is 103.1% of the original rent.
103.1% of 拢460 = 拢460 梅 100 脳 103.1 = 拢474.26
Cai's new rent is 拢474.26 pcm.
Elin
Decrease is 3.5%, so new rent is 96.5% of original rent.
96.5% of 拢484 = 拢484 梅 100 脳 96.5 = 拢467.06.
Elin's new rent is 拢467.06 pcm.
Calculating the original value after a discount has been applied may be useful to find out what the item was priced at before.
Example
A shirt has been reduced by 20% and now costs 拢50. How much did it cost originally?
Solution
Taking the original price to be 100% we can see that the sale price is 80% of this value because 100% 鈭 20% = 80%.
100% 鈭 20% = 80%.
拢50 = 80%.
Divide both sides by 80 to find 1%.
拢0.625 = 1%.
Multiply both sides by 100 to find the original price.
Original price is 拢62.50.
We can check this by working out 80% of the original price, and checking that it is the sale price.
80% of 拢62.50 = 拢62.50 梅 100 脳 80 = 拢50, which is correct.