*IBPS Test Bank Exam Quant Notes : Ratio and proportion is a very general topic for all bank exams. Mostly bank exams includes this topic in quantitative section.*

**Also read -**###
**Quantitative Shortcuts:Ratio and Fractions **

**Ratio is a quantity which represents the relationship between two similar quantities. It expresses a magnitude by which quantity is multiple of another one. Ratio is represented as 2:3 or 2/3. Here, numerator i.e. 2 is known as "ANTECEDENT" and denominator i.e. 3 is known as "CONSEQUENT".**If antecedent is more than the consequent, then it is known as improper ratio and if less ,then it is known as proper ratio.

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### Some important points:

**1.**If ratio is written as A:B, it is said to be a linear form and in case it is written as A/B, it is said to be fractional form.

**2.**Ratio does not have any unit. It is mere number.

**3.**The equality of two ratios is known as proportion i.e. a/b = c/d

If a/b = c/d , then it is also equal to a+c/b+d

**Invertendo**: If a/b = c/d , then b/a = d/c

**Alterendo**: If a/b = c/d , then a/c = b/d

**Componendo**: If a/b = c/d , then a+b/b = c+d/d

**Dividendo**: If a/b = c/d , then a-b/b = c-d/d

Componendo and Dividendo : If a/b = c/d , then a+b/a-b = c+d/c-d

**4.**If a/b = b/c = c/d =...... so on, then a,b,c,d... are in G.P.

Proof: Let a/b = b/c = c/d =k

c= dk, b= ck, a= bk

Therefore, b= dk^2 and a= dk^2

All are in G.P.

**5.**If a>b and same positive number is added to each term, then ratio decreases.

For example: a/b = 4/3 = 1.3, If 2 is added to each term, then a/b = 4+2/3+2 = 6/5 = 1.2

Therefore, ratio decreases.

**6.**If a

**For example: a/b = 3/4 = 0.7, If 2 is added to each term, then a/b = 3+2/4+2 = 5/6 = 0.8**

Therefore, ratio increases.

a^2:b^2 is duplicate ratio of a:b

a^3:b^3 is triplicate ratio of a:b

a^1/2:b^1/2 is sub-duplicate ratio of a:b

a^1/3:b^1/3 is sub-triplicate ratio of a:b

a and d are known to be extremes

b and c are known to be means.

Therefore, ratio increases.

**7.**If we multiply or divide any number, there will be no effect on ratio.**8.**Let a:b is a ratioa^2:b^2 is duplicate ratio of a:b

a^3:b^3 is triplicate ratio of a:b

a^1/2:b^1/2 is sub-duplicate ratio of a:b

a^1/3:b^1/3 is sub-triplicate ratio of a:b

**9.**Proportions i.e. a:b = c:da and d are known to be extremes

b and c are known to be means.

**10.**In a:b :: c:d, d is fourth proportional to a,b and c.**11.**If x is third proportional to a,b then it is written as a:b :: b:x.**Problem**: 94 is divided into two parts in such a way that the fifth part of second are in ratio 3:4. The first part is?**Solution**: Let these parts are A and B

A/5 = 3 , This implies, A = 15

B/8 4 B 32

1st part = 94*15 = Rs30

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