# Percentage: Concept, Formulae & Shortcuts

The concept of percentage is important not only for the quantitative aptitude section but also for the Data Interpretation (DI) and Data Sufficiency section of the competitive exams.

So, let us understand the basic Concepts of Percentage.

**Percentage** can be divided into per-cent-age that means ‘per every hundred’. It is denoted by the symbol %.

For instance if a student scores 20 out of 25, his score out of 100 is given by multiplying the fraction by 100.

That is,

Thus, any given ratio can be converted into percentage by multiplying the ratio with hundred, and the vice versa to convert percentage into decimal or fraction.

**PERCENTAGE CHANGE**

There are two changes when a quantity gets modified. They are

- Actual change
- Percentage change

For example, when the price of a product goes up from Rs 100 to Rs 120, the actual change is Rs 20. This is given by Rs 120-Rs 100.

The Percent change can be calculated by,

Thus, the percentage rise in value can be given by

**Relationship between percentage and ratio:**

There is a direct relationship between the numerator of a ratio and the ratio itself. If the numerator increases by a certain percentage, the ratio also increases by the same percentage,

Note: if the denominator remains constant.

For example, 25/40 is 25% more than 20/40. (As the rise in numerator (5) is 25% of its initial value (20))

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**Percentage required nullifying a percentage rise:**

If there is a percentage rise then the effect of its change can be nullified by

** **

For Example: If the price of a product went up by 25% by what percentage should the price be reduced to make the price even?

Percentage reduction required=

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**Successive percentage change:**

If a value A increases by a%, b%, c% and so on upto n%, the total rise in % is given by the formula,

**Final output = **

If a value A decreases by a%, b%, c% and so on upto n%, the total decline in % is given by the formula,

**Final output = **

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