# Quant Study Notes: Percentage

**Dear Readers,**

Today we’ll discuss about Percentage. This topic is can fetch you marks easily but you need to know the right concepts and types of questions to practice.

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**All about Percentage**

**Percentage**means per hundred when we say 50% of a number it means half of the number. Similarly, 25% of a number is one fourth of the number; 20% means one fifth of the number, 16.67% means one sixth of a number etc. Hence percentage indicates the part or fraction of a number.

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**Percentage and Ratio**

Following table gives equivalence relation between commonly used fractions and their equivalent percentagesSome times using fractions is better than using actual percentage.

**☞**For example to calculate 14.28% of 343, we should not directly use multiplication, we can use equivalent fractions of 14.28% i.e. 1/7 hence the required answer

**Example:**

**Calculate 30% of 710**

**Method 2:-**

In this method we will learn a different approach.

Any number is always 100% of itself

So the 100% of 710 is = 710

10% of 710 is = 71.0

1% of 710 is = 7.10

0.1% of 710 is = 0.710

We require 30% of 710, which is = 3 × 10% of 710

= 3 ×71 = 213

**Multiplying factor: - (MF)**

M.F. can also be used in D.I. to a huge extent.

Since ratio of 48 to 36 is 4/3=1.333….,

We can say that 48 is 33.33% more than 36.

**∴ Initial value × M.F. = final value**

**Successive Increment/Decrement**

**☞**Suppose a number is increased or decrease by x% then by y%, if the initial value of the number is n, then it’s final value

**☞**Alternatively, we can use the successive change formula,

Effective percentage increase or decrease

**☞**If a quantity changes by three consecutive changes of x%, y% and z%, then the effective percentage change

**Percentage Points**

**Percentage point is used to simplify the data in percentage point and it is defined as difference of two percentage figures for example if a man spends 10% of his salary in the month of January and 25% in the month of February, then we can say that expenditure increases by 15 percentage point and percentage increase is:**

(Assuming that his salary remains constant)

**Example:**

A mixture of 40 liters of milk and water contains 10% water. How much water should be added to it so that water may be 20% in the new mixture?

**Types of Questions for Percentage**

This topic is incorporated mainly in three types of questions:

**✔ Simplification**

**✔ Data Interpretation**

**✔****Word Problems****Practice Percentage Questions**

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