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

Let the number to be subtracted be x. So, new numbers are 23 - x, 30 - x, 57 - x, 78 - x

Since, these numbers are in proportion,

$\therefore \dfrac{23 - x}{30 - x} = \dfrac{57 - x}{78 - x} \\[0.5em] \Rightarrow (23 - x)(78 - x) = (57 - x)(30 - x) \\[0.5em] \Rightarrow (1794 - 23x - 78x + x^2) = (1710 - 57x - 30x + x^2) \\[0.5em] \Rightarrow x^2 - x^2 - 101x + 87x + 1794 - 1710 = 0 \\[0.5em] \Rightarrow -14x + 84 = 0 \\[0.5em] \Rightarrow 14x = 84 \\[0.5em] \Rightarrow x = 6.$

Hence, the number that must be subtracted to make the numbers in proportion is 6.