How To Solve Percentage Problems

In mathematics, a percentage is a number or ratio that tin exist expressed every bit a fraction of 100. If we have to calculate percent of a number, divide the number by the whole and multiply past 100. Hence, the percentage means, a function per hundred. The word per cent means per 100. It is represented by the symbol "%" .

Percentage

Examples of percentages are:

10% is equal to 1/10 fraction
20% is equivalent to ⅕ fraction
25% is equivalent to ¼ fraction
fifty% is equivalent to ½ fraction
75% is equivalent to ¾ fraction
ninety% is equivalent to 9/10 fraction

Percentages have no dimension. Hence it is chosen a dimensionless number. If nosotros say, 50% of a number, then it means 50 per cent of its whole.

Percentages can also be represented in decimal or fraction grade, such as 0.vi%, 0.25%, etc. In academics, the marks obtained in any subject field are calculated in terms of percent. Like, Ram has got 78% of marks in his last test. So, this per centum is calculated on account of the total marks obtained by Ram, in all subjects to the total marks.

Per centum Formula

To determine the percentage, we have to divide the value by the total value and so multiply the resultant by 100.

Per centum formula = (Value/Total value)× 100

Example: two/5× 100 = 0.4 × 100 = forty per cent

How to calculate the percentage of a number?

To summate the per centum of a number, we need to utilise a different formula such every bit:

P% of Number = X

where Ten is the required pct.

If we remove the % sign, then nosotros demand to express the to a higher place formulas as;

P/100 * Number = 10

Example: Calculate 10% of 80.

Allow 10% of 80 = X

ten/100 * fourscore = X

X = 8

Percentage Difference Formula

If we are given with two values and we need to discover the percentage difference between these 2 values, and then information technology tin can exist done using the formula:

$\begin{array}{l}Percent~Difference = \frac{\left|N_{1}-N_{2}\right|}{\left[\frac{\left(N_{one}+N_{two}\right)}{2}\right]} \times 100\stop{array} $

For instance, if 20 and 30 are two dissimilar values, then the percentage difference between them volition be:

% difference between 20 and thirty =

$\begin{array}{fifty}Percentage~Divergence = \frac{\left|20-30\right|}{\left[\frac{\left(20+thirty\right)}{ii}\right]} \times 100\end{array} $

Percentage Increment and Subtract

The percentage increment is equal to the subtraction of the original number from a new number, divided by the original number and multiplied by 100.

% increase = [(New number – Original number)/Original number] ten 100

where,

increment in number = New number – original number

Similarly, a percentage subtract is equal to the subtraction of a new number from the original number, divided past the original number and multiplied past 100.

% decrease = [(Original number – New number)/Original number] x 100

Where decrease in number = Original number – New number

So basically if the answer is negative and then there is a percentage subtract.

Solved Example

Two quantities are generally expressed on the basis of their ratios. Hither, allow us empathise the concepts of percentage through a few examples in a much better way.

Example: Allow a handbag contain ii kg of apples and 3kg of grapes. Discover the ratio of quantities present, and the percentage occupied by each.

Solution:

The number of apples and grapes in a handbag can be compared in terms of their ratio, i.e. 2:3.

The actual interpretation of percentages can exist understood as follows:

The same quantity can be represented in terms of the per centum occupied, which can be done equally given beneath.

Total quantity present = 5 kg

Ratio of apples (in terms of total quantity)= 2/5

$\begin{array}{l}=\frac{ii}{5} \times \frac{100}{100}\terminate{array} $

From the definition of percentage, it is the ratio that is expressed per hundred,

(ane/100) = ane%

Thus, Percentage of Apples = (2/five)× 100 = 40%

Percentage of Grapes = (3/5)× 100 = lx%

Percent Chart

The percentage nautical chart is given hither for fractions converted into percentages.

Fractions	Per centum
one/two	50%
1/iii	33.33%
1/iv	25%
ane/5	20%
ane/half dozen	16.66%
i/seven	xiv.28%
i/8	12.5%
1/9	11.11%
1/10	10%
1/eleven	9.09%
ane/12	8.33%
1/13	seven.69%
one/14	7.fourteen%
one/xv	6.66%

Converting Fractions to Percentage

A fraction can exist represented past a/b.

Multiplying and dividing the fraction by 100, we have

$\brainstorm{array}{50}\frac{a}{b} \times \frac{100}{100} =\left ( \frac{a}{b} \times 100 \right ) \frac{1}{100}…(i)\end{assortment} $

From the definition of percent, we accept;

(ane/100) = 1%

Thus, equation (i) can be written as:

(a/b)× 100%

Therefore, a fraction tin can be converted to a percentage only past multiplying the given fraction by 100.
Too, read: Ratio To Per centum

Per centum Questions

Q.ane: If 16% of 40% of a number is viii, then find the number.

Solution:

Allow Ten be the required number.

Therefore, every bit per the given question,

(16/100) × (40/100) × X = 8

So, X = (8 × 100 × 100) / (16 × xl)

= 125

Q.two: What percentage of 2/7 is 1/35 ?

Solution:

Let X% of two/vii is i/35.

∴ [(ii/7) / 100] × X = 1/35

⇒ X = (1/35) × (seven/2) × 100

= 10%

Q.3: Which number is 40% less than 90?

Solution:

Required number = threescore% of 90

= (90 10 60)/100

= 54

Therefore, the number 54 is xl% less than 90.

Q.four: The sum of (xvi% of 24.2) and (10% of ii.42) is equal to what value?

Solution:

Equally per the given question ,

Sum = (16% of 24.two) + (10% of ii.42)

= (24.2 × 16)/100 + (two.42 × 10)/100

= iii.872 + 0.242

= 4.114

Give-and-take Issues

Q.1: A fruit seller had some apples. He sells 40% apples and still has 420 apples. Originally, he had how many apples?

Solution:

Let he had N apples, originally.

Now, as per the given question, we accept;

(100 – xl)% of N = 420

⇒ (60/100) × N = 420

⇒ N = (420 × 100/lx) = 700

Q.two: Out of ii numbers, 40% of the greater number is equal to threescore% of the smaller. If the sum of the numbers is 150, and so the greater number is?

Solution:

Allow X exist the greater number.

∴ Smaller number = 150 – X {given that the sum of ii numbers is 150}

Co-ordinate to the question,

(forty × Ten)/100 = threescore(150 – 10)/100

⇒ 2p = 3 × 150 – 3X

⇒ 5X = iii × 150

⇒ X = xc

Divergence between Percentage and Pct

The words percentage and percent are related closely to each other.

Percent ( or symbol %) is accompanied by a specific number.

E.1000., More than 75% of the participants responded with a positive response to abjure.

The per centum is represented without a number.

E.g., The percentage of the population afflicted by malaria is betwixt threescore% and 65%.

Fractions, Ratios, Percents and Decimals are interrelated with each other. Let us look at the conversion of one form to another:

South.no	Ratio	Fraction	Percent(%)	Decimal
1	i:1	i/one	100	i
2	1:2	1/ii	50	0.5
3	1:3	1/three	33.333	0.3333
4	1:four	1/4	25	0.25
5	1:five	ane/v	xx	0.xx
6	1:half-dozen	1/6	16.667	0.16667
7	one:7	1/7	14.285	0.14285
eight	1:eight	1/8	12.five	0.125
nine	i:9	1/9	11.111	0.11111
10	1:ten	1/x	10	0.10
11	1:11	ane/11	9.0909	0.0909
12	1:12	1/12	viii.333	0.08333
13	1:13	1/13	7.692	0.07692
14	1:14	1/14	seven.142	0.07142
xv	ane:xv	1/15	6.66	0.0666

Pct in Maths

Every percent problem has iii possible unknowns or variables :

Per centum

Part

Base

In order to solve whatsoever percentage problem, you lot must exist able to place these variables.

Look at the following examples. All iii variables are known:

Example 1: 70% of thirty is 21

70 is the percentage.

30 is the base.

21 is the role.

Example two: 25% of 200 is 50

25 is the per centum.

200 is the base.

fifty is the part.

Example iii: 6 is fifty% of 12

six is the part.

l is the percentage.

12 is the base.

Percentage Tricks

To calculate the percentage, we tin use the given below tricks.

Example- Evidence that 10% of thirty is equal to 30% of 10.

Solution- ten% of xxx = iii

30% of x = 3

Therefore, they are equal i.east. ten % of y = y % of 10 holds true.

Marks Percentage

Students get marks in exams, ordinarily out of 100. The marks are calculated in terms of per cent. If a student has scored out of total marks, then nosotros have to divide the scored marks by total marks and multiply by 100. Let u.s.a. come across some examples here:

Marks obtained	Out of Full Marks	Pct
xxx	100	(30/100) × 100 = 30%
ten	xx	(10/20) × 100 = l%
23	50	(23/50) × 100 = 46%
13	xl	(13/twoscore) × 100 = 32.5%
90	120	(90/120) × 100 = 75%

Bug and Solutions

Question i:- Suman has a monthly salary of $1200. She spends $280 per month on food. What percentage of her monthly bacon does she save?

Solution:

Suman'southward monthly salary = $1200

Savings of Suman = $(1200 – 280) = $ 920

Fraction of salary she saves = 920/1200

Percentage of salary she saves = (920/1200)× 100 = 920/12% = 76.667%

Question 2:- Below given are 3 grids of chocolate. What percent of each White chocolate bar has a Nighttime chocolate bar?

Problems on Percentage

Solution:

Each grid above has 100 white chocolate blocks. For each white chocolate bar, the ratio of the number of nighttime chocolate boxes to the total number of white chocolate confined can exist represented equally a fraction.

(i) 0 dark and 100 white.

i.e., 0 per 100 or 0%.

(two) fifty dark and l white.

i.e., 50 per 100 or fifty%.

(iii) 100 dark and 0 white.

i.e., 100 per 100 or 100%.

Frequently Asked Questions – FAQs

What exercise y'all mean by per centum?

In maths, a percent is a value or ratio that shows a fraction of 100. Percent means per 100. It does not take any units.

What is the symbol of percentage?

Percentage is denoted by '%' symbol. Information technology is also termed as per cent.

What is the pct formula?

The formula to calculate the pct of a number out of another number is:
Percentage = (Original number/Another number) x 100

What is the percentage of 45 out of 150?

What is 40% of 120?

xl% of 120
= (40/100)× 120
= 48