Use Of Percentages
Interpreting Percentages
We saw how percentages were helpful in comparison. We have also learnt to convert fractional numbers and decimals to percentages. Now, we shall learn how percentages can be used in real life. For this, we start with interpreting the following statements:
5% of the income is saved by Ravi. — 20% of Meera’s dresses are blue in colour.
Rekha gets 10% on every book sold by her.
What can you infer from each of these statements?
By 5% we mean 5 parts out of 100 or we write it as
Converting Percentages to “How Many”
EXAMPLE 5
A survey of 40 children showed that 25% liked playing football. How many children liked playing football?
- Here, the total number of children are 40.
- To find the numerical value of 25% of 40 we do:
x - Solving the value is found to be
- Hence, 10 children out of 40 like playing football.
EXAMPLE 6
Rahul bought a sweater and saved Rs. 200 when a discount of 25% was given. What was the price of the sweater before the discount?
- Given that: 25% of original price is equal to Rs. 200
- Let the original price be P.
- To solve, we write the equation:
x = - Solving the value of P is found to be
- Evaluating
- Therefore, the original price of the sweater is Rs. 800.
Ratios to Percents
Sometimes, parts are given to us in the form of ratios and we need to convert those to percentages. Consider the following example:
EXAMPLE 7
Reena’s mother said, to make idlis, you must take two parts rice and one part urad dal. What percentage of such a mixture would be rice and what percentage would be urad dal?
- In terms of ratio we would write this as Rice : Urad dal =
: - Writing the ratio in fractions, we get: Fraction of rice in mixture =
- Fraction of urad dal in mixture =
- Converting the respective fractions into percentages, we get: Percentage of rice =
% - Then, percentage of urad dal =
% - Thus, we have found the respective values
EXAMPLE 8
If ₹ 250 is to be divided amongst Ravi, Raju and Roy, so that Ravi gets two parts, Raju three parts and Roy five parts. How much money will each get? What will it be in percentages?
SOLUTION The parts which the three boys are getting can be written in terms of ratios as 2 : 3 : 5. Total of the parts is 2 + 3 + 5 =
| Amounts received by each | Percentages of money for each |
|---|---|
| Ravi gets | |
| Raju gets | |
| Roy gets | |
Increase or Decrease as Per Cent
There are times when we need to know the increase or decrease in a certain quantity as percentage. For example, if the population of a state increased from 5,50,000 to 6,05,000. Then the increase in population can be understood better if we say, the population increased by 10 %.
How do we convert the increase or decrease in a quantity as a percentage of the initial amount? Consider the following example.
EXAMPLE 9
A school team won 6 games this year against 4 games won last year. What is the per cent increase?
- The increase in the number of wins (or amount of change) =
- Percentage increase = (
/ ) x 100 % - Therefore, percent of increase =
% - We found the answer.