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Ratio and Proportion | CA CPT Maths | CMA Foundation Maths Video Lectures


Ratio and Proportion | CA CPT Maths | CMA Foundation Maths Video Lectures 


Watch This Full video for Complete learning on Ratio and Proportion CA Foundation Notes Maths Video Lectures. Get all your CA Foundation Ratio and Proportion Questions and Answers on this CA Foundation Video Lectures. 


What is Ratio?

A Ratio is a comparison of the sizes of two or more quantities of the same kind by division.

If a and b are two quantities of the same kind (in same units), then the fraction a/b is called the ratio of a to b.


What is an Inverse Ratio?

One Ratio is the inverse of another if their product is 1. Thus a:b is the inverse of b: a and vice versa.


What is Proportion?

An equality of two ratios is called a proportion.

For quantities a,b,c,d are said to be  in proportion  if a:b= c:d

Properties of Proportion-

 

1. Alternendo

If a : b = c : d, then a : c = b : d.

ab = cd

Multiply both sides by bc ; ab x bc = cd x bc

ac = bd 

a : c = b : d


2. Componendo

If a : b = c : d, then a + b : b = c + d : d

ab = cd

Adding 1 to both sides, we get

ab + 1 = cd + 1

a+bb = c+dd

⇒ a + b : b = c + d : d


3. Dividendo

If a : b = c : d then a - b : b = c - d : d

ab = cd

Subtracting 1 from both sides, we get

ab - 1 = cd - 1

a−bb = c−dd

⇒ a - b : b = c - d : d


4. Componendo and Dividendo-

If a : b = c : d then a + b : a - b :: c + d : c - d.

a : b = c : d

 a + b : b = c + d : d by componendo

a - b : b = c - d : d by dividendo

Dividing,

 a+bb ÷ a−bb = c+dd ÷ c−dd

 a+bb x ba−b = c+dd x dc−d

 a+ba−b = c+dc−d

 ⇒ a + b : a - b = c + d : c - d

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