What number must be added to each of the numbers 4, 6, 8, 11 in order to get the four numbers in proportion ?

Let the number to be added to numbers be x.

∴ 4 + x : 6 + x :: 8 + x : 11 + x

$\Rightarrow \dfrac{4 + x}{6 + x} = \dfrac{8 + x}{11 + x} \\[1em] \Rightarrow (4 + x)(11 + x) = (8 + x)(6 + x) \\[1em] \Rightarrow 44 + 4x + 11x + x^2 = 48 + 8x + 6x + x^2 \\[1em] \Rightarrow x^2 + 15x + 44 = x^2 + 14x + 48 \\[1em] \Rightarrow x^2 - x^2 + 15x - 14x = 48 - 44 \\[1em] \Rightarrow x = 4.$

Hence, the number to be added to make numbers proportional is 4.