Question

When the greater of the two numbers increased by 1 divides the sum of the numbers, the result is 3/2. When the difference of these numbers is divided by the smaller, the result is 1/2. Find the numbers.

Answer 1

Let the two numbers be a and b respectively such that $b>a$
according to given condition,
$\frac{a+b}{b+1}=\frac{3}{2}$
$\Rightarrow 2a+2b=3b+3$
$\Rightarrow 2a-b=3.....\left(i\right)$
Also,
$\frac{b-a}{a}=\frac{1}{2}$
$\Rightarrow 2b-2a=a$
$\Rightarrow 2b-3a=0.........\left(ii\right)$
Multiplying (i) by $2$ we get
$4a-2b=\mathrm{6.....}\left(iii\right)$
adding (ii) and (iii) we get
$a=6$
Substituting $a=6$ in (i) we get
$2\left(6\right)-b=3$
$\Rightarrow 12-b=3$
$\Rightarrow b=9$
Thus the two numbers are $6$ and $9$ respectively.