# Continued Proportion

**Continued proportion :**Three numbers ‘a’, ‘b’ and ‘c’ are said to be continued proportion if a, b and c are in proportion.

Thus, if a, b and c are in continued-proportion, then

a,b,b,c are in proportion, that means

**a : b : : b : c**

⇒ Product of extremes = Product of means

⇒ a x c = b x b

⇒ a x c = b

^{2}

Continued-proportion is also known as

**mean proportional**.

If ‘b’ is a mean proportional between a and c then b

^{2}= ac.

**Examples :**

1) Find the mean proportional between 9 and 25.

**Solution :**

Let x be the mean proportional between 9 and 25.

⇒ x

^{2}= 9 x 25

⇒ x

^{2}= 225

⇒ x = 15

Hence, the mean proportional between 9 and 25 is 15.

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2) If 3, x , 12 are in continued-proportion, find the value of x.

**Solution :**

Since 3,x,12 are in continued-proportion,

3,x,x,12 are in proportion.

Product of extremes = Product of means

⇒ 3 x 12 = x . x

⇒ 36 = x

^{2}

⇒ x = 6.

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3) If 40, x, x, 40 are in proportion, then find the value of x.

**Solution :**

Product of means = product of extremes

x. x = 40 x 40

⇒ x

^{2}= 1600

⇒ x = 40

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4) If we divide 20 between Jacob and Ariel in the ratio 3 : 2, how much will each of them get? what number is a mean proportional between those parts?

**Solution :**

Sum of the two terms of the ratio (3 : 2) =3 + 2 = 5

Jacob's share = (3/5) x 20 = 12

Ariel's share =(2/5) x 20 = 8

Mean proportion of 12 and 8 is √(12 x 8)

⇒ √(96)

⇒ √(16 x 6)

⇒ 4√6

**Ratio - Proportion**

• Ratio and Proportion

• Ratio in the simplest form

• Comparison of ratios

• Equivalent ratios

• Proportion

• Continued Proportion

• Ratio and Proportion

• Ratio in the simplest form

• Comparison of ratios

• Equivalent ratios

• Proportion

• Continued Proportion

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