Explanation

(d)
Let the two numbers be $a$ and $b$
$\therefore\ a - b = 48$ and $\frac{a + b}{2} - \sqrt{ab} = 18$
$\Rightarrow \left( \sqrt{a} - \sqrt{b} \right)\left( \sqrt{a} + \sqrt{b} \right) = 48$
and $\left( \sqrt{a} - \sqrt{b} \right) = 6$
$\Rightarrow \sqrt{a} + \sqrt{b} = 8$ and $\left( \sqrt{a} - \sqrt{b} \right) = 6$
$\Rightarrow \sqrt{a} = 7$ and $\sqrt{b} = 1$
$\Rightarrow a = 49$ and $b = 1$
Hence, the greater number is 49.