What must be added to each of the number 711 and 19 so that the resulting number may be in continued proportion?

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Question 10 Ratio and Proportion Exercise 7.2

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Answer:

Consider x be added to each number

16 + x , 26 + x and 40 + x are in continued proportion

It can be written as

(16 + x)/ (26 + x) = (26 + x)/ (40 + x)

By cross multiplication

(16 + x) (40 + x) = (26 + x) (26 + x)

On further calculation

\begin{array}{l} 640+16 x+40 x+x^{2}=676+26 x+26 x+x^{2} \\ 640+56 x+x^{2}=676+52 x+x^{2} \\ 56 x+x^{2}-52 x-x^{2}=676-640 \end{array}

So we get

4x = 36

x = 36/4 = 9

Hence, 9 is the number to be added to each of the numbers.

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What must be added to each of the numbers 7, 11 and 19, so that the resulting numbers may be in continued proportion?

Explanation:

Let X be the required number, then (7 + X) : (11 + X) :: (11 +X) : (19 + X) (7 + X) (19 + X) = (11 + X)2 X2 + 26X + 133 = X2 + 22X + 121

4X = - 12 or X = - 3

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