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

2. Learning Objectives
What is
proportion
Properties of
Proportion
and its
application
2

3. Proportion
• An equality of two ratio is called a proportion / Four
quantities a, b, c, d are said to in the proportion if a : b = c : d
(also written as a : b :: c : d) i.e. a/b = c/d i.e. if ad = bc.
• The term a and d are called extremes, the term b and c are
called the means. The fourth term d is called the fourth
proportional of a, b and c taken in order.
• If a:b :: b:c, then a, b, c are called in continued proportion, b
is called the mean proportional between a and c and c is
called the third proportional of a and b.
3

4. Properties - Cross-multiplication
4

5. Properties - Invertendo
5

6. Properties - Alternendo
6

7. Properties - Compounendo
7

8. Properties - Dividendo
8

9. Properties - Compondeo and
Dividendo
9

10. Properties - Sum of antecedents to
the Sum of consequents
10

11. Properties - Sum of antecedents to
the Sum of consequents - Continued
Hence, each (a + c + e + ….) : (b + d + f …….) is equal to
each ratio
or
In words - If any number of ratios be equals to one another,
then each of these ratio is equal to ratio of the sum of
antecedents to the sum of consequents
11

12. Illustration - 13
12

13. Illustration - 14
13

14. Illustration - 15
14

15. Illustration - 16
15

16. Illustration – 16 – Continued
16

17. Illustration – 16 – Continued
17

18. Illustration - 17
18

19. Illustration - 18
19

20. Illustration – 18 - Continued
20

21. Illustration - 19
21

22. Illustration - 20
22

23. Illustration 21
The price of a scooter and a moped are in the ratio 9 : 5. If
a scooter costs Rs. 6800 more than a moped, the price of
scooter is?
(a) Rs. 17,000 (b) Rs. 13600 (c) Rs. 15300 (d) None of
these
Solution
Scooter : Moped = 9 : 5
Let cost of scooter is 9x and cost of moped is 5x.
23

24. Illustration 21 - Continued
24

25. Illustration - 22
25

26. Illustration – 22 - Continued
26

27. Illustration 23
A sum of Rs. 9300 is divided among A,B and C in such a
way that share of A and B are in the ratio of 1 : 3 and those
of B and C are in the ratio 4 : 5. The amount received by C
is
(a) 1200 (b) 3600 (c) 4500 (d) 5000
Solution
A : B = 1 : 3, B : C = 4 : 5
Multiplying terms of first ratio by 4 and second ratio by 3 we
get
A : B = 4 : 12, B : C = 12 : 15
27

28. Illustration 23 - Continued
28

29. Illustration 24
If p : q = 1 : 3 and a : b = 4 : 3, then the value of
4pa + 3qb : 9pa + 4qb is
(a) 41 : 82 (b) 27 : 82 (c) 43 : 72 (d) None of these
Solution
p : q = 1 : 3 and a : b = 4 : 3
Taking the Compounded ratio of LHS and RHS i.e.
29
econsequencofProduct
santecedentofProduct
=RatioCompounded

30. Illustration 24 – Continued
30

31. Illustration - 25
31

32. Illustration – 25 - Continued
32

33. Illustration – 26
A man divides his property in such manner that his son’s
share to his wife’s share and wife’s share to his daughter’s
share are both in the ratio 3 : 1. If the daughter gets Rs.
10,000 less than the son, then the total worth of his
property is
(a) Rs. 16,250 (b) Rs. 18,250 (c) Rs. 15,250 (d) Rs.
21,250
Solution
Let a = Son’s share ;
b= Wife’s Share;
c=Daughter’s share
33

34. Illustration – 26 – Continued
34

35. Illustration – 26 – Continued
35

36. Illustration 27
36

37. Illustration 28
37

38. Illustration – 29
The sum of the ages of 3 persons is 150 years. 10 years
ago their ages were in the ratio 7 : 8 : 9. Their present ages
are
(a) (45,50,55) (b) (40,60,50) (c) (35,45,70) (d) None of
these
Solution
Let the ages of the three persons 10 years ago be 7x, 8x
and 9x.
Their present ages will be 7x+10, 8x+10 and 9x+10
38

39. Illustration – 29 – Continued
The sum of their present ages is
7x + 10 + 8x + 10 + 9x + 10 = 150
24x =150 – 30
24 x = 120
x = 5
Therefore present ages are 7X5+10, 8X5+10, 9X5+10
(45, 50, 55)
39

40. Illustration – 30
40

41. Illustration – 30 – Continued
41

42. Thank You
42