Proportion – Finding Missing Value

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’.

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

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

= 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

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