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# Find Two Numbers Whose Mean Proportional is 18 and the Third Proportional is 486. - ICSE Class 10 - Mathematics

#### Question

Find two numbers whose mean proportional is 18 and the third proportional is 486.

#### Solution

Let a and b be the two numbers, whose mean proportional is 18.

therefore "ab" = 182 => "ab" = 324 => "b" = 324/"a" ......(i)

Now, third proportional is 486

∴ a : b : : b : 486

⇒ b2 = 486 a

⇒ (324/"a")^2 = 486  a

⇒ (324)^2/"a"^2 = 486 a

⇒ "a"^3 = (324 xx 324)/486

⇒ a3 = 216

⇒ a = 6

b = 324/"a" = 324/6 = 54

Therefore, numbers are 6 and 54 .

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#### APPEARS IN

Frank Solution for Frank Class 10 Mathematics Part 2 (2016 to Current)
Chapter 9: Ratio and Proportion
Exercise 9.2 | Q: 15

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Solution Find Two Numbers Whose Mean Proportional is 18 and the Third Proportional is 486. Concept: Proportions.
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