A ratio is a comparison of two numbers. We generally separate the two numbers in the ratio with a colon ":". Suppose we want to write the ratio of 8 and 12.

We can write this as 8:12 or as a fraction 8/12, and we say the ratio is eight to twelve.

- The ratio of two quantities a and b of same units is the fraction x/y, where b ? 0
- The fraction x/y can be represented as x:y

The concept of ratio & proportion is used in quantitative as well as DI section. Grocery shopping, selling, cooking to industries production- everything makes use of the concept of ratio, proportion & mixtures. Partnership assumes significance in the business world, where various business partners need to distribute profits according to their share of investments and time period. Here, you will learn the formulae & shortcuts to solve questions based on ratio, mixtures and partnership.

It is the ratio of squares of two numbers.

It is the ratio between square roots of two numbers.

It is the ratio of cubes of two numbers.

It is the ratio between cube roots of two numbers

It is the ratio of product of first terms in every ratio to that of product of second term in every ratio.

**For example: **
Compound ratio of (a : x), (b : y), (c : z) is (abc : xyz)

The ratio formed by interchanging their old places in the ratio to new

The inverse ratio of 5 : 8 is 8 : 5.

## Proportion:- 1) Proportion is the equality of two ratios.
When (a : b = x : y) is represented as (a : b :: x : y), then a, b, x, y are said to be in proportion. In (a : b :: x : y), a and y are called as extremes and b and x are called as mean terms. Product of means = Product of extremes - 2) Mean proportion: Mean proportion between x and y is given as xy
- 3) Third proportion: If p : q = q : s, then s is called as third proportional to p and q.
- 4) Fourth proportion: If u : v = x : y, then y is the fourth proportional of u, v and x.
## Quick Tips and Tricks## 1) Comparison of ratios:## 2) Proportion## 4) Variation:- If a = kb for some constant k, then we can say that a is directly proportional to b.
- If ba =k for some constant k, then we can say that a is inversely proportional to b.
## 5) Ratio between first and second quantityIf ratio between first and second quantity m : n = a : x, second and third quantity n : p = b : y, fourth and fifth quantity p : q = c : z, then m : n : p : q can be easily solved by using the trick shown below: 6) If a number a is divided in the ratio x : y, |

- Numbers
- Highest Common Factor And Least Common Multiple
- Decimal
- Fractions
- Simplification
- Surds And Indices
- Chain Rule
- Square Root And Cube Root
- Ratio And Proportion
- Pipes And Cisterns
- Boats and Streams
- Problems on Trains
- Alligation or Mixtures
- Time and Distance
- Geometry
- Time and Work
- Simple Interest
- Problem Solving

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- Direct and Indirect Speech
- Geometry
- Fractions
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- Synonyms
- How to Structure Sentences in an Essay
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