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1. Ratio and Proportion,
Indices and Logarithm
Paper 4: Quantitative Aptitude Chapter 1
Part I: Ratio & Proportion
Ms. Ritu Gupta, MA (Maths.)

2. Ratio
2

3. Learning Objectives
How to
compute
and
compare
two ratios
Effect of
increase or
decrease of
a quantity
on the ratio
The concept
and
application
of different
kinds of
ratio
3

4. Ratio
A ratio is a comparison of the sizes of two or more quantities of
the same kind (in same units) by methods of division.
If a and b are two quantities of the same kind then the fraction
a/b is called the ratio of a to b.
It is written as a : b or a/b
The quantities a and b are called the terms of the ratio, a is
called the first term or antecedent and b is called the second
term or consequent.
4

5. Points to Remember
1
• Both terms of a ratio can be multiplied or divided by the same (non –
zero) number. Usually a ratio is expressed in the lowest form or the
simplest form. Example:- 10 : 15 = 10/15 = (5×2)/ (5×3) = 2/3 = 2:3
2
• Ratio exists only between quantities of the same kind. For Example:
There is no ratio between the height of a child and the salary of a
teacher.
3
• The order of the terms in a ratio is important. For example - 4:5 ≠ 5:4
4
• If a quantity increases or decreases in the ratio a : b, then new quantity =
b of the original quantity / a
5

6. Points to Remember - 2
Raju’s weight is 48.8 kg. If he reduces his weight in the ratio of 8:7, find his new weight.
Solution: Original weight of Raju = 48.8 kg
He reduces his weight in the ratio 8:7
His new weight = (7 × 48.8) / 8
= 42.7 kg
6
5
• The fraction by which the original quantity is multiplied to
get a new quantity is called the factor multiplying ratio.

7. Points to Remember - 3
Example
Ratio between 1 hour and 20 minutes
= Ratio between (1x60) min. and 20 min.
= 60 / 20 = 3/1 = 3:1
7
6
• Quantities to be compared (by
division) must be in the same units.

8. Points to Remember - 4
8
7
• To compare two ratios, convert them into equivalent like
fractions.

9. Different Kinds of Ratio- Inverse Ratio
9

10. Different Kinds of Ratio- Ratio of
Equality
• A ratio a : b is said to be of greater equality if a > b, of less
equality if a<b and of equality if a = b.
Example
10
7 : 4 is a ratio of greater equality
5 : 9 is a ratio of less equality
5 : 5 is ratio of equality

11. Different Kinds of Ratio- Compounded
Ratio
11

12. Different Kinds of Ratio- Duplicate
Ratio
• A ratio compounded to itself is called its duplicate ratio.
Thus a² : b² is the duplicate ratio of a : b.
Example
Duplicate ratio of 5 : 7 is 52 : 72 = 25 : 49
12

13. Different Kinds of Ratio- Triplicate
Ratio
• The compounded ratio of a ratio with its duplicate ratio is
called its triplicate ratio. Thus a³ : b³ is the triplicate ratio of
a : b
Example
Triplicate ratio of 2 : 3 is 23 : 33 = 8 : 27
13

14. Different Kinds of Ratio- Sub –
Duplicate Ratio
14

15. Different Kinds of Ratio- Sub –
Triplicate ratio
15

16. Different Kinds of Ratio - Continued
Ratio
• Continued Ratio is the relation (comparison) between the
magnitudes of three or more quantities of the same kind.
The continued ratio of three similar quantities a, b, c is
written as a : b : c
Example
The continued ratio of 200, 400 and 600 is
200 : 400 : 600 = 1 : 2 : 3
16

17. Different Kinds of Ratio -
Commensurable Ratio
• If the ratio of two similar quantities can be expressed as a
ratio of two integers then the quantities are called
commensurable e.g. 3:4
17

18. Different Kinds of Ratio -
Incommensurable Ratio
18

19. Illustration 1
19

20. Illustration 2
The ratio compounded of duplicate ratio of 4:5, triplicate
ratio of 1:3. sub duplicate ratio of 81:256 and sub triplicate
ratio of 125:512 is
(a) 4 : 512 (b) 3 : 32 (c) 1 : 120 (d) None of these
Solution
The duplicate of ratio of 4 : 5 is
42 : 52 = 16 : 25
The triplicate ratio of 1 : 3 is
13 : 33 = 1 : 27
20

21. Illustration 2- Continued
21

22. Illustration 3
22

23. Illustration- 4
23

24. Illustration- 5
24

25. Illustration- 5- Continued
25

26. Illustration- 6
26

27. Illustration- 6- Continued
27

28. Illustration- 7
28

29. Illustration- 8
A bag contains Rs. 187 in the form of 1 Rupee, 50 paise
and 10 paise coins in the ratio of 3 : 4 : 5. Find the number
of each type of coins.
(a) 102, 136, 170 (b) 136, 102, 170 (c) 170, 102, 136
(d) None of these
Solution
Let the number of 1 Rupee, 50 paise and 10 paise coins be
3x, 4x and 5x respectively. Then,
29

30. Illustration- 8- Continued
30

31. Illustration- 9
31

32. Illustration- 10
32

33. Illustration - 11
Find in what ratio will the wages of the employees in a
workshop be increased or decreased if there is a reduction
in the number of employees in the ratio 7 : 4 and an
increment in their wages in the ratio 16 : 21.
(a) 2 : 7 (b) 4 : 3 (c) 4 : 1 (d) 7 : 3
Solution
Let the original number of employees be x.
Therefore the number of employees after reduction will be
4x/7.
Let the (average) wages per worker be y
33

34. Illustration – 11- Continued
34

35. Illustration – 11- Continued
35

36. Illustration - 12
The ratio of the number of boys to the number of girls in a
dance school of 360 students is 3 : 5. If 15 new girls are
admitted to the dance school, find how many new boys
should be admitted so that the ratio of the number of boys
to the number of girls becomes 4 : 5.
(a) 75 (b) 57 (c) 55 (d) 45
Solution
Let the number of boys and number of girls be 3x and 5x
Therefore 3x+5x = 360
36

37. Illustration – 12- Continued
37

38. Illustration – 12- Continued
38

39. Thank You
Please see next part for e-Lecture on
Proportion