Ratio and proportion is a very general topic for all bank exams. Mostly bank exams includes this topic in quantitative section.
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.
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<b and same positive number is added to each term, then ratio increases.
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.
7) If we multiply or divide any number, there will be no effect on ratio.
8) Let a:b is a ratio
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
9) Proportions i.e. a:b = c:d
a 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.
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.
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<b and same positive number is added to each term, then ratio increases.
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.
7) If we multiply or divide any number, there will be no effect on ratio.
8) Let a:b is a ratio
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
9) Proportions i.e. a:b = c:d
a 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
47
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
47
