What number must be deducted from each of the numbers 8/10 17 and 22 so that the remainder numbers will become proportional?

What number should be subtracted from each of the numbers 23, 30, 57 and 78 so that the remainders are in proportion ?

Let x be subtracted from each term, then23 – x, 30 – x, 57 – x and 78 – x are proportional23 – x : 30 – x : : 57 – x : 78 – x⇒ `(23 – x)/(30 – x) = (57 – x)/(78 – x)`⇒ (23 – x) (78 – x) = (30 – x) (57 – x)

⇒ 1794 – 23x – 78x + x2 = 1710 – 30x – 57x + x2

Hence 6 is to be subtracted.

Concept: Concept of Proportion

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Question 7 Ratio and Proportion Exercise 7.2

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Answer:

Consider x be subtracted from each term

23 – x, 30 – x, 57 – x and 78 – x are proportional

It can be written as

23 – x: 30 – x :: 57 – x: 78 – x

(23 – x)/ (30 – x) = (57 – x)/ (78 – x)

By cross multiplication

(23 – x) (78 – x) = (30 – x) (57 – x)

By further calculation

\begin{array}{l} 1794-23 x-78 x+x^{2}=1710-30 x-57 x+x^{2} \\ x^{2}-101 x+1794-x^{2}+87 x-1710=0 \end{array}

So we get

-14x + 84 = 0

14x = 84

x = 84/14 = 6

Therefore, 6 is the number to be subtracted from each of the numbers.

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