1. Proportion – Finding Missing Value

2. Recap
When two ratios a:b and c:d are equal, then the ratios are said to be in proportion. It is denoted as a:b :: c:d. It is read as ‘a is to b’ as ‘c is to d’.

3. Recap
When two ratios are in proportion, i.e., a:b :: c:d, then the product of means is equal to the product of extremes. Here, b and c are means and a and d are extremes
a : b :: c : d
Product of means = b x c
Product of extremes = a x d
Means
Product of means = Product of extremes
b x c = a x d
Extremes

4. 2 : 5 :: k : 20 5 x k = 2 x 20 k = 2 x 20 5 k = 40 = 8 5 Ans: k = 8
Example 1: If the ratios formed using the numbers 2, 5, k, 20 in the same order are in proportion, then ‘k’ is ____
Solution:
Given:
2, 5, k, 20 are in proportion
To find:
Value of k
2 : 5 :: k : 20
We know that when the ratios are in proportion,
Product of means = Product of extremes
2 : 5 :: k : 20
5 x k
= 2 x 20
Means k
= 2 x 20
Extremes 5 8 k
= 40
= 8 5
Ans: k = 8

5. = 3 x 30 m = 3 x 30 6 m 6 3 : 6 :: m : 30 = 90 = 15 6 x m Ans: m = 15
Example 2: If the ratios 3:6 and m:30 are in proportion, then ‘m’ is ___
Solution:
Given:
2, 5, k, 20 are in proportion
To find:
Value of k
3 : 6 :: m : 30
We know that when the ratios are in proportion,
Product of means = Product of extremes
3 : 6 :: m : 30
Means
6 x m
= 3 x 30
Extremes m
= 3 x 30 6 15 m
= 90
= 15
Ans: m = 15 6

6. Try these
If the ratios 4:12 and m:9 are in proportion, then the value of m is?