As a mathematical number, the percentage is written or expressed out of a total of 100. The sign "%" percent represents percentage and also indicates that the denominator is 100. The percentage gives us information corresponding to the ratios and proportions. Quite often, it becomes a lot easier to use and understand differences when we make use of percentages instead of fractions with varying denominators.
For comparison purposes, a percentage is a simple method of standardizing different quantities. Therefore, we can say that the concept of percentage has many real applications in the different situations of our everyday lives. Suppose that a bag contains 2 kg of apples and 3 kg of mangoes. We have to find the percentage occupied by each fruit. So, we will start by finding out the total quantity of fruits present in the bag, which is 2 + 3 = 5 kg. Therefore, the percentage of apples in the bag = (2/5) * 100 = 40, and the percentage of mangoes in the bag = (3/5) * 100 = 60. Thus, we can say that the bag has 40% apples and 60% oranges.
Percentages are widely used in several other fields like in the financial world for calculating the interest rates, in academics for calculating students' grades at school or college, etc. We not only represent data in percentage but also indicate the increase and decrease of value in percentage.
Solved Examples On Percentage:
Question 1
Ram has a monthly salary of Rs 30,000. He spends 10,000 on his expenses. What percentage of this monthly salary does he save?
Answer:
Given that – Ram’s monthly salary = Rs 30,000
Amount of money spent on his expenses = Rs 10, 000
Amount of money he saves = Rs 30,000 – Rs 10,000 = Rs 20,000
Percentage of salary he saves = (20,000/30,000) * 100 = 66.67%
Thus, Ram saves 66.67% of his salary every month.
Question 2
What percentage of 30 is 21?
Answer:
Let the percentage be X.
So, according to the question, (X/100)*30 = 21
30X/100 = 21
X = (21 * 100)/30
X = 70%
Hence, 70% of 30 is 21.
Question 3
Show that 10% of 40 is equivalent to 40% of 10.
Answer:
10% of 40 = (10/100)*40 = 4
40% 10 = (40/100)* 10 = 4
Hence, they are equal.
Percentile
The mathematical concept of percentile refers to the value below which a percentage of data falls. It is extensively used for determining the performance of a person relative to the others, and for calculating weight, income, and many other things. For instance, in examinations, the concept of percentile shows where a candidate stands w.r.t other candidates. The percentile formula is mentioned below:
Percentile = (Number of values below "X"/Total Number of all the Values) * 100
Solved Examples:
Question 1
The scores for students are given as 41, 46, 47, 55, 63, 69, 74, 76, 82, and 93. Find the percentile for score 69.
Answer:
Number of scores below 69 = 5
Total number of scores = 10
We have to calculate the percentile for score 69.
The formula is given as:
Percentile = (Number of values below "X"/Total Number of all the Values) * 100
Let's substitute the known values in the formula.
Percentile = (5/10)*100 = 50
PERCENTAGE | PERCENTILE |
It is a number represented out of 100. | It is not a number represented out of 100. |
It is not a value below which a definite number of values are found. | It is a value below which a definite number of values are found. |
It is written or expressed as n%. | It is written or expressed as nth. |
It doesn’t have quartiles (which divides the number of data points into quarters). | It has quartiles (which divides the number of data points into quarters). |
It is not based on ranked numbers. | It is based on ranked numbers. |
It can be written or expressed in the form of a decimal. | It can’t be written or expressed in the form of a decimal |
It can be written or expressed in the form of a ratio or proportion. | It can’t be written or expressed in the form of a ratio or proportion. |
It is based on only a single case. | It is based on a comparison of 1 case along with all the cases in a particular situation. |
It doesn’t depend on a normal distribution. | It depends on a normal distribution. |
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