This is a basic question from ML aggarwal book of class 10th, chapter 7, ratio and proportion., ICSE board

In this question we have been given four numbers, and we are asked to find the number that can be subtracted in all the four numbers in order to make them in proportion.

Question 7, 7.2

Solution: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

1794 – 23x – 78x + x

^{2}= 1710 – 30x – 57x + x^{2}x

^{2}– 101x + 1794 – x^{2}+ 87x – 1710 = 0So we get

– 14x + 84 = 0

14x = 84

x = 84/14 = 6

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