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If three numbers a, b and c are in continued proportion, then

a : b : : b : c
For example: If 3 : 15 : : 15 : 75, then 3, 15 and 75 are in continued proportion.
Example 20: If 48, 24, x are in continued proportion, find the value of x?

Solution: We have, 48, 24, and x are in continued proportion.
So, 48 : 24 :: 24 : x

We have, Product of extremes = Product of means
48 × x = 24 × 24
24 24
×
x = = 12
48
Thus, the value of x is 12.
Example 21: Find x if x, 8 and 16 are in continued proportion.
Solution: We have, x, 8, and 16 are in continued proportion.

So, x : 8 : : 8 : 16
We have, Product of extremes = Product of means
x × 16 = 8 × 8
88 64
×
x = = = 4
16 16
Thus, the value of x is 4.

Mean Proportion

If a, b, and c are in continued proportion, then b is called the mean proportion of a and c.
Therefore, a : b : : b : c
2
Product of extremes = Product of means If b = ac, where b is the
a × c = b × b mean proportion of a and
a × c = b 2 c, then a, b, c will be in
continued proportion.
or b = ac
2

Life Skills
In a grocery shop you may simply illustrate ratios while checking the prices of different groceries by utilising
2 different boxes of cereal. You can see the relationship between the amount & the size by dividing number of
the ounces of cereal by the price. If a 10-ounce box of cereal costs `300 and a 20-ounce box costs `500, which
box offers a better price per ounce, and how do you calculate it? How do you see the relationship between the
amount and the size of cereals? [ounce (oz) is a unit of measuring weights, 10 oz = 0.02835 kg = 28.35 g]

Example 22: Find the mean proportion between 18 and 8?
Solution: Given a = 18 and c = 8

2
We know that if b is the mean proportion between a and c, then b = ac
\ b = 18 × 8
2
b = 144 = 12 × 12
2
b = 12
Thus, the mean proportion between 18 and 8 is 12.

Mathematics-7 210