If antecedent is more than the consequent, then it is known as improper ratio and if less ,then it is known as proper ratio.
Meritmock Recommended Study notes for Ratio and Proportions
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Some important points:
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 aFor 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?
A/5 = 3 , This implies, A = 15
B/8 4 B 32
1st part = 94*15 = Rs30