Question

If the same number be added to the numbers $5,11,15$ and $31$, the resulting numbers are in proportion. Find the number.

Answer 1

Let The number be $x$

$\frac{5+x}{11+x}=\frac{15+x}{31+x}$

$\Rightarrow 155+x^2+36x=165+x^2+26x$

$10x=10$

$x=1$

$\therefore$ Numbers are $5+1=6$, $11+1=12$

$15+1=16$, $31+1=32$.