Problems based on Numbers Test 5

Let the number be 10x + y; then
xy = 8 ...(i)
Also, 10x + y + 18 = 10y + x
⇒ 9(x – y) = – 18
⇒ x – y = – 2 ...(ii)
Now,${\left(\mathit{x}+\mathit{y}\right)}^2={\left(\mathit{x}-\mathit{y}\right)}^2+4\mathit{x}\mathit{y}$ $={\left(-2\right)}^2+4\times 8=36$
$\therefore \mathit{x}+\mathit{y}=6$ ...(iii)
Solving the equations (ii) and (iii) we get, x = 2 and y = 4
Hence, number = 10 × 2 + 4 = 24