# Proportion and Ratio

Proportion and Ratio define proportion, Proportion question, proportion formula. Proportion is a part of Proportion and Ratio.

### Introduction Proportion and Ratio

Proportion is a part of Proportion and Ratio and Proportion is a statement that two ratios are equal. Thus, it is involved four quantities and these four quantities are said to be in proportion. When the ratio of first two is equal to the ratio of last two and
symbol used to denote proportion is ::.
e.g:- Let a:b is a ratio and c:d is an another ratio then the proportion is a:b::c:d. a*d =b*c.
The 1st term and the 4th term are called as extremes and the 2nd and 3rd term is called as middle term or means.
i.e:- a*d = b*c or Product of extremes = Product of means

### Properties of Proportion

• If x is the third proportional a and b, then a:b :: b:x
• Mean proportion of a and b is square root of a*b.
• If x is the fourth proportion of a, b and c, then a:b :: c:x.

### Continued proportion

If in a proportion, the middle terms are equal, then it is called as continued proportion.
e.g:- If a:b = b:c or a:b :: b:c, then the number a,band c are called continued proportion. This also known as the proportion of three numbers. Here middle term b is known as mean proportion and c is called third proportion.

### Question Based On Proportion

• 1:9 :: 9:x find the value of x.

(a) 9                  (b) 81
(c) 1                  (d) 5

• 0.75 : x :: 5 : 8, find the value of x.

(a) 1.5               (b) 1.8
(c) 1.6               (d) 1.4

• 3 : 5 :: 60 : x, find the value of x.

(a) 80                (b) 81
(c) 82                (d) 84

• a : b = 7 : 9 and b : c = 3 : 5, then what is the value of a : b : c

(a) 7 : 9 : 15       (b) 21 : 35 : 45
(c)  7 : 9 : 5        (d) 7 : 3 : 15

• 10, 20,  x, and 40 are in the proportion, then what is the value of x?

(a) 5                   (b) 20
(c) 30                 (d) 40

• The third proportion of 12 and 30 is

(a) 40                  (b) 45
(c) 60                  (d) 75

• The fourth proportion of 4, 9 and 12

(a) 36                     (b) 48
(c) 27                     (d) 108

• 12 : 27 :: 8 : fourth term

(a) 16                      (b) 18
(c) 20                      (d) 24

• What will be the mean proportion of the term 64 and 225 ?

(a) 240                     (b) 60
(c) 120                     (d) 80

• What will be the mean proportion of 9 and 16?

(a) 54                        (b) 12
(c) 10                        (d)84

• What is the mean proportion of 18 and 72 ?

(a) 18                        (b) 36

(c) 108                      (d) 90