Question

What number must be added to each of 9,42,3and18 so that sum will be in proportion

Answer 1

let number added be x
Hence
$\frac{9 + x}{42 + x} = \frac{3 + x}{18 + x} \\ (9 + x)(18 + x) = (3 + x)(42 + x) \\ {x}^{2} + 27x + 162 = {x}^{2} + 45x + 126 \\ 18x = 36 \\ x = 2$
Hence number added so that they are in proportion is 2