Problems based on Numbers Test 1

Let the ten's place digit and unit's place digit be x and x + 2.
Then, number = 10x + x + 2 = 11x + 2;
Sum of the digits = x + x + 2 = 2x + 2
Now, $\left(11\mathit{x}+2\right)\left(2\mathit{x}+2\right)=144$
$\Rightarrow 22{\mathit{x}}^2+26\mathit{x}+4=144$
$\Rightarrow 11{\mathit{x}}^2+13\mathit{x}-70=0$
$\Rightarrow \left(\mathit{x}-2\right)\left(11\mathit{x}+35\right)=0$
Hence, $\mathit{x}=2$
∴ Number = 10 × 2 + 2 + 2 = 24