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Converting Percentages to “How Many”

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Example

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. Out of these, 25% like playing football. 

(i) 25% of 40

Number of children who like playing football = `25/100` × 40 = 10.

(ii) Out of 100, 25 like playing football So out of 40,

Number of children who like playing football = `25/100` × 40 = 10.

Hence, 10 children out of 40 like playing football.

Example

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?

Rahul has saved Rs. 200 when price of sweater is reduced by 25%. This means that 25% reduction in price is the amount saved by Rahul.

(i) 25% of the original price = Rs. 200

Let the price (in Rs.) be x.

So, 25% of x = 200 or `25/100 xx x = 200`

or, `x/4` = 200 or x = 200 × 4

Therefore, x = 800.

(ii) Rs. 25 is saved for every Rs. 100

Amount for which Rs. 200 is saved = `100/25 xx 200` = Rs. 800

Thus both obtained the original price of sweater as Rs. 800.

Example

For summative evaluation in a certain school, 720 of the 1200 children were awarded A grade in Maths. What is the percentage of students getting A grade?

Suppose the students getting A grade are A%.

`"A"/100 = 720/1200`

∴ `"A"/100 xx 100 = 720/1200 xx 100`

∴ A = 60

∴ 60% students got A grade.

Example

A certain Organization adopted 18% of the 400 schools in a district. How many schools did it adopt?

Here, 18% means 18 schools adopted out of a total of 100.
The total number of schools is 400.
Suppose the number of schools adopted is A.

`"A"/400 = 18/100`

`"A"/400 xx 400 = 18/100 xx 400`

∴ A = 72.

∴ The number of schools adopted is 72.

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