Page 102 - New Medley 5 Semester 2

Product of means in Product of extremes in

I. 5 × 10 = 50 I. 2 × 25 = 50

II. 12 × 6 = 72 II. 8 × 9 = 72

III. 7 × 21 = 147 III. 1 × 147 = 147
In each of the three cases, we see that

Product of means = Product of extremes

i.e., a × d = b × c

Out of the four terms, if any three are given, we can find the fourth using

the above relation.

Example 4: Are the numbers 1, 2, 3 and 6 in proportion?
Solution: Ratio of 1 and 2 is 1 : 2. Ratio of 3 and 6 is 3 : 6, i.e., 1 : 2.

The two ratios are equal, therefore 1, 2, 3 and 6 are in
proportion, i.e., 1 : 2 : : 3 : 6.

Alternative Method

The four terms are 1, 2, 3 and 6.

Product of means = 2 × 3 = 6

Product of extremes = 1 × 6 = 6

Since product of means = product of extremes

So, 1 : 2 : : 3 : 6

Example 5: The first, second and third terms of a proportion are 9,

15 and 12. Find the fourth term.

Solution: Let the fourth term of the proportion be d.

So, 9 : 15 : : 12 : d

We know product of means = Product of extremes

i.e., 15 × 12 = 9 × d

5 4
15 × 12
 d = = 5 × 4 = 20
9 3 1

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