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 + x2 = 1710 – 30x – 57x + x2
x2 – 101x + 1794 – x2 + 87x – 1710 = 0
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