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# PERCENTAGE: IMPORTANT FACTS AND FORMULAE

## Percentages and Fractions: Aptitude Tips and Hints, Theory, Facts and Formula

In this section the theory, tips hints and formulae of percentage and fraction, aptitude has been explained with solved examples which will be useful for practicing the aptitude questions of all the difficult questions of all difficulty levels.

## How to practice percentages as Aptitude Problem Point of view?

Practice online questions on aptitude from the percentages section of Lofoya.com. Three levels of difficulty on aptitude problems with answers are provided on percentages which will be useful for MBA and similar competitive exams. Regular practice of these percentage online solved aptitude questions is essential for good score in the competitive exams.

## Percentage questions in MBA exams

Percentage and fraction is a very important topic asked in the various competitive exams and MBA exams like CAT, MAT, GMAT, XAT etc. Regular online practice of these aptitude problems with detailed solution to each question is essential to good score.

## Practice Percentage (Aptitude) for MBA Exams

Percentage and fraction problems section as a subsection of Aptitude is provided on this page with solved examples for better understanding of concepts. Aspirants for CAT, GRE, GMAT, TANCET, IIFT, MAT, SAT, TOEFL, XAT, SNAP, XLRI, IRMA, IELTS, JMET, FMS, NMAT, Bank PO, SBI PO, Bank Clerk, Teaching Exam, NMIMS etc. and other MBA exams will find this percentage theory and examples relevant and very useful.

This is the aptitude questions and answers section on "Percents and Fraction " with detailed explanation for various interview, competitive examination and entrance test. Problems of three difficulty levels are given with detailed solution description, explanation, so that it becomes easy to grasp the fundamentals.

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## Percentage

The word percent can be understood as follows:
Per cent => for every 100.
So, when percentage is calculated for any value, it means that you calculate the value for every 100 of the reference value. When you see the word "percent" or the symbol %, remember it means $1/100$. For example,
$20 \text"percent" = 20% = 20*(1/100) = 1/5$

## Why Percentage?

Percentage is a concept evolved so that there can be a uniform platform for comparison of various things. (Since each value is taken to a common platform of 100)

Example: To compare three different students depending on the marks they scored we cannot directly compare their marks until we know the maximum marks for which they took the test. But by calculating percentages they can directly be compared with one another.

## 1. Concept of Percentage:

By a certain percent, we mean that many hundredths. Thus x percent means x hundredths, written as x%.

To express x% as a fraction: We have , $x% = x/100.$
Thus,$20% =20/100 =1/5; 48% =48/100 =12/25$ etc.
To express $a/b$ as a percent: We have,$a/b =(a/b)*100%$
Thus, $1/4 =[(1/4)*100] = 25%; 0.6 =6/10 =3/5 =[(3/5)*100]% =60%.$

## 2. Commodity Price Increase/Decrease:

If the price of a commodity increases by R%, then the reduction in consumption so as not to increase the expenditure is:
$[(R/(100+R))*100]%$

If the price of the commodity decreases by R%, then to maintain the same expenditure by increasing the consumption is:
$[(R/(100-R))*100]%$

## 3. Results on Population:

Let the population of the town be P now and suppose it increases at the rate of R% per annum, then:

1. Population after n years $= P [1+(R/100)]^n$
2. Population n years ago$= P /[1+(R/100)]^n$

## 4. Results on Depreciation:

Let the present value of a machine be P. Suppose it depreciates at the rate R% per annum. Then:

1. Value of the machine after n years $= P[1-(R/100)]^n$
2. Value of the machine n years ago $= P/[1-(R/100)]^n$
5. If A is R% more than B, then B is less than A by
$[(R/(100+R))*100]%$
If A is R% less than B , then B is more than A by
$[(R/(100-R))*100]%$

## Percentages – Fractions Conversions:

For faster calculations we can convert the percentages or decimal equivalents into their respective fraction notations. The following is a table showing the conversions of percentages and decimals into fractions:

10%

0.1

1/10

12.5%

0.125

1/8

16.66%

0.1666

1/6

20%

0.2

1/5

25%

0.25

1/4

30%

0.3

3/10

33.33%

0.3333

1/3

40%

0.4

2/5

50%

0.5

1/2

60%

0.6

3/5

62.5%

0.625

5/8

66.66%

0.6666

2/3

70%

0.7

7/10

75%

0.75

3/4

80%

0.8

4/5

83.33%

0.8333

5/6

90%

0.9

9/10

100%

1.0

1

## Converting decimals:

We can go for converting decimals more than 1 from the knowledge of the above cited conversions as follows:

We know that $12.5% = 0.125 = 1/8$
Then, $1.125 = [8(1)+1]/8 = 9/8$ (i.e., the denominator will add to numerator once, denominator remaining the same.

Also, $2.125 = [8(2)+1]/8 = 17/8$ (here the denominator is added to numerator twice)
$3.125 = [8(3)+1]/8 = 25/8$ and so on.

Thus we can derive the fractions for decimals more than 1 by using those less than 1.
We will see how use of fractions will reduce the time for calculations:

Example: What is 62.5% of 320?

Solution: Value = $(5/8)*320$(since$62.5% = 5/8$)= 200.

## Important Points to Note:

When any value increases by

10%, it becomes 1.1 times of itself. (since 100+10 = 110% = 1.1)

20%, it becomes 1.2 times of itself.

36%, it becomes 1.36 times of itself.

4%, it becomes 1.04 times of itself.

Thus we can see the effects on the values due to various percentage increases.

When any value decreases by

10%, it becomes 0.9 times of itself. (Since 100-10 = 90% = 0.9)

20%, it becomes 0.8 times of itself

36%, it becomes 0.64 times of itself

4%, it becomes 0.96 times of itself.

Thus we can see the effects on a value due to various percentage decreases.

Note: 1. When a value is multiplied by a decimal more than 1 it will be increased and when multiplied by less than 1 it will be decreased.

2. The percentage increase or decrease depends on the decimal multiplied.

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Example: When the actual value is x, find the value when it is 30% decreased.

Solution: 30% decrease => 0.7 x.

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Example: A value after an increase of 20% became 600. What is the value?

Solution: 1.2x = 600 (since 20% increase)

=> x = 500.

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Example: If 600 is decrease by 20%, what is the new value?

Solution: new value = 0.8 * 600 = 480. (Since 20% decrease)

Thus depending on the decimal we can decide the % change and vice versa.

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Example: When a value is increased by 20%, by what percent should it be reduced to get the actual value?

Solution: (It is equivalent to 1.2 reduced to 1 and we can use % decrease formula)

$% \text"decrease" = ({1.2 – 1}/1.2)*100 = 16.66%$

When a value is subjected multiple changes, the overall effect of all the changes can be obtained by multiplying all the individual factors of the changes.

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Example: The population of a town increased by 10%, 20% and then decreased by 30%. The

new population is what % of the original?

Solution: The overall effect = 1.1 * 1.2 * 0.7 (Since 10%, 20% increase and 30% decrease)

= 0.924 = 92.4%.

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Example: Two successive discounts of 10% and 20% are equal to a single discount of ___

Solution: Discount is same as decrease of price.

So, decrease = 0.9 * 0.8 = 0.72 => 28% decrease (Since only 72% is remaining)