Learning Percentage without Mathematical Formulae
With glimpses of real-life scenarios
Entrance season in Nepal
This is the season of entrance preparation for the students who had completed their +2. My sister, Bishakha, is preparing for her engineering entrance examination, and her roommate Prakriya is also preparing for her medical entrance examination. They both gave their weekly exams. I asked my sister about the marks she obtained on her weekly exam and she replied she got 330 out of 370 and Prakriya got 223 out of 260 in her weekly examination. I was curious about who got the highest percentage on the weekly examinations.
What is the percentage?
Percent means per cent that is per hundred(out of hundred). Percentage is the ratio when some number is normalized such that the denominator is 100. It is denoted by the ‘ %’ sign. Percentage is a pure number and doesn't have any unit of measurement.
Numbers to percentage
To convert the marks obtained by Bishakha and Parkriya to percentage, I need to reduce their full marks to 100, so the method I used is:
For Bishakha,
330/370 = 33/37 (diving both by 10)
To change the denominator to 100, I divide the denominator by 37 and then multiply by 100. We must do the same operation in the numerator.
=> (33 / 37) * 100 / (37 / 37) * 100 = 89.18 / 100 i.e. 89.18%
So, the percentage of Bishakha is 89.18%.
Now for Parkriya, following the same process:
223 / 260 = (223 / 260) * 100 / (260 / 260) * 100 = 85.76 / 100 i.e 85.76%
So, the percentage of Parkriya is 85.76%.
In this way, we can find the percentage obtained by Bishakha and Parkriya without employing any formula. So, I concluded Bishakha got the highest percentage than Parkriya.
Percentage to number
I had a share of 750,000 USD in XYZ company. XYZ company announced a 15% bonus of their share to every shareholder in the Annual General Meeting. I was curious how much amount I would get from XYZ company as a bonus. So I decided to convert my bonus percentage to a number.
15% means 15 per cent i.e. 15 out of 100 = 15 USD bonus / 100 USD share.
Now, we need to find the total bonus in my 750k USD share.
in 15 % in 750,000 is I get 15% out of 750000 bonus.
For converting a number to a percentage, we reduce the denominator to 100. Now, to convert the percentage to a number, we reduce the denominator to the number (i.e 750000 USD).
Now, the calculation would be:
15% of my share:
(15 / 100 * 750,000) / (100 /100 * 750,000) = 112,500/ 750,000
So, 15% of 750,000 is 112,500.
So, the amount of bonus I will get from my share is 112,500 USD.
Percentage of increase/decrease
In the above paragraphs, we talked about changing a number to a percentage and vice versa. Now, let’s talk about the percentage of increase/decrease.
Let’s take an example of a shopkeeper who sells KitKat chocolate at the price of 20 NPR, whose actual price is 10 INR. The shopkeeper sold it at the double price of INR price while the actual price of KitKat is 10* 1.6 = 16 NPR. So, the shopkeeper increased the price by 4NPR in each KitKat.
To find the percentage of increase, we can have the ratio of the increased amount to the actual amount and then use the same process of reducing the denominator to 100.
So, the process goes as:
increased amount / actual price = 4/16
Dividing by 4 on both numerator and denominator,
increased amount / actual price = 1 / 4
To reduce the denominator to 100, we multiply both the numerator and denominator by 25.
=>increased amount / actual price = (1 * 25) / (4 * 25) = 25 / 100 i.e. 25%
So, we find out that shopkeeper increases 25% on its actual price.
Let’s take yet another example.
The shopkeeper sells dairy milk chocolate of 50 INR for 100 NPR. The actual price of dairy milk is 50* 1.6 = 80 NPR but the shopkeeper increased it by 100 - 80 = 20 NPR.
Now finding the percentage of increase:
20 / 80 = 1 / 4 = 1 * 25 / 4 * 25 = 25 / 100 = 25%
So, we find out that the shopkeeper increases the price of the dairy milk by 25% in this case too.
I showed both examples to my sister. She was curious if every chocolate imported from India gets its price increased by 25% by the shopkeeper.
Showing her all the instances and proving them would be infeasible. So, to prove my claim of a 25% increase, I formulated a mathematical scenario.
Let's take the price of an item ABC as x INR and it was sold on 2x NPR . But the actual price is x * 1.6 = 1.6x NPR. The increased amount is 2x - 1.6x = 0.4x NPR
Now, let's find out the percentage increase:
0.4 x / 1.6 x = 4 / 16 = 1 * 25 / 4 * 25 = 25 / 100 = 25%
Hence, I worked out and proved that, if the shopkeeper sold the item in double of INR price, the shopkeeper had actually increased the item price by 25%.
Summing up
To find the percentage we need not remember the formula. Formulas are helpful and handy to solve mathematical problems. However, it might be hard to memorize them all the time. Today, we showed how percentages can be worked out using their definition and simple logic.
I hope this article helps you and makes your life easier while doing any kind of percentage calculation.
