Profit and Loss
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October 8, 2022About this post
Ratio and Proportion is a very important topic with application in data interpretation, allegation and mixture. In this section you will learn about
- Ratio and its types
- Proportion and its relation with ratio
- Operations that will help in solving problems on Ratio and Proportion
- Solved question and answers to improve your skills
The first lesson in this topic is an introduction to ratio and proportion. We shared some formulae that will be required to tackle problems onratio and proportion. The exercises contain solved question and answers. When solving exercises, we recommend you to try solving the problems on your own, that way you will understand better and you can define your own approach to solving problems on ratio and proportion.
Introduction to Ratio and Proportion
Ratio :
Ratio is the comparison of two quantities of same kind. If A and B are two quantities then,
- The ratio of A to B is represented by A : B and its value is $\frac{A}{B}$
- The first term A is called the Antecedent and the second term B is called the consequent
- A : B has no unit
- If we multiply or divide the terms of the ratio by the same non-zero number, the resulting value will still be the same.
Proportion :
It is a statement that equates two ratios.
Example : $\frac12 =\frac24$
- A proportion is represented using the symbol “::”.
i.e A : B = C : D is represented as A : B :: C : D.
In the above statement,
- A and D are called Extremes, B and C are called Means.
- D is the fourth proportional to A, B and C
Note:
Product of the means = Product if the extremes.
=> A x D = B x C
- If $\frac AB = \frac BC$
Here, B is called the mean proportional and C is called the third proportional
- If $\frac AB =\frac CD$, then $\frac AB =\frac CD = \frac{A+C}{B+D}$
- Invertendo:
If $\frac AB = \frac CD$, then $\frac BA = D/C$
- Altrendo:
If $\frac AB = \frac CD$, then $\frac AC = \frac BD$
- Componendo:
If $\frac AB = \frac CD$, then $\frac{A+B}{B} = \frac{C+D}{D}$
- Dividendo:
If $\frac{A}{B} = \frac{C}{D}$, then $\frac{A-B}{B} = \frac{C-D}{D}$
- Componendo and Dividendo:
If $\frac AB = \frac CD$, then $\frac{A+B}{A-B} = \frac{C+D}{C-D}$
- Types of Ratio
- Duplicate Ratio:
Duplicate ratio of two numbers A and B is the ratio of their squares, i.e $\frac{A^2}{B^2}$
- Triplicate Ratio
Triplicate ratio of two numbers A and B is the ratio of their cubes, i.e $\frac{A^3}{B^3}$
- Sub-duplicate Ratio
Subduplicate ratio of two numbers A and B is the ratio of their square roots, i.e $\frac{\sqrt{a}}{\sqrt{b}}$
- Sub-triplicate Ratio
Sub-triplicate ratio of two numbers A and B is the ratio of their cube roots, i.e $\frac{\sqrt[3]{A}}{\sqrt[3]{B}}$
- Inverse or Reciprocal Ratio
Inverse ratio of A and B is $\frac{1}{A} : \frac{1}{B}$