During the following ideas I will be suggesting a variety of methods for solving certain percentages problems. Those involving calculators are invariably quicker, however will fail on a non-calculator paper.
The value of a TV was increased by 10%. It has a new value of £440 after the 10% increase. What did it cost originally?
To solve this problem, we follow these logical steps.
STEP 1: Let us call the original value that we want to find 100%
STEP 2: After a 10% increase the new amount is therefore 110%
STEP 3: We know that this new 110% percent corresponds to a value of £440
STEP 4: Because 110% = £440
Divide by 110 so 1% = £4
STEP 5: The original cost was 100%.
100% = 100 × 1% = 100 × £4 = £400
Another way of doing it, using a calculator, is to do £440 ÷ 1.10
Dividing by 1.10 reverses the 10% to give the original cost
Suppose that the number of people in a village increased by 15%. There are now 299 people.
How many people were there before the increase.
We will apply the same logical steps as before
STEP 1: Let us call the original amount of people that we want to find 100%
STEP 2: After a 15% increase the new amount of people is therefore 115%
STEP 3: We know that this new 115% percent corresponds to 299 people
STEP 4: Because 115% = 299 people
Divide by 115 so 1% = 2.6 people
STEP 5: The original number of people we called 100%.
100% = 100 × 1% = 100 ×2.6 = 260 people.
Calculator method: 299 ÷ 1.15 = 260
A Computer was decreased by 14% in a sale. It now costs £344. How much did it cost before the reduction?
We will mimic the steps from before:
STEP 1: Let us call the original value that we want to find 100%
STEP 2: After a 14% decrease the new amount is therefore 86%
STEP 3: We know that this new 86 percent corresponds to a value of £344
STEP 4: Because 86% = £344
Divide by 86 so 1% = £4
STEP 5: The original cost was 100%.
100% = 100 × 1% = 100 × £4 = £400
Calculator method: £334 ÷ 0.86 = £400
The 0.86 corresponds to the 14% ( ie 1.0-0.14 = 0.86) decrease
A TV costs £293.75. This includes VAT. How much VAT has been added?
STEP 1: VAT is an additional 17.5% so £293.75 corresponds to 100% + 17.5% = 117.5%
STEP 2: We find 1% by dividing £293.75 by 117.5 to get 1% = £2.50
STEP 3: VAT equals 17.5%. So VAT equals 17.5 × £2.50 = £43.75