It is a question from ML aggarwal, class 10th, chapter 7, ratio and proportion, Avichal publication

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

Question 6, 7.2

Solution:Consider x to be added to 5, 11, 19 and 37 to make them in proportion

5 + x: 11 + x :: 19 + x: 37 + x

It can be written as

(5 + x) (37 + x) = (11 + x) (19 + x)

By further calculation

185 + 5x + 37x + x

^{2}= 209 + 11x + 19x + x^{2}185 + 42x + x

^{2}= 209 + 30x + x^{2}So we get

42x – 30x + x

^{2}– x^{2}= 209 – 18512x = 24

x = 2

Hence, the least number to be added is 2