Explanation

(a)
Let two numbers be p and Q.
$\therefore$Given, $\frac{2PQ}{P + Q} = 14\frac{2}{5} = \frac{72}{5}$ ….(i)
And $\sqrt{PQ} = 24 \Rightarrow PQ = 576\ \ \ \ \ \ldots(ii)$
From Eq.(i),
$P + Q = \frac{10PQ}{72}$
$\Rightarrow P + Q = \frac{10 \times 576}{72} = 80\ \left\lbrack from\ Eq.(ii) \right\rbrack\ldots(iii)$
Now, $(P - Q)^{2} = (P = Q)^{2} - 4PQ$
$= 80^{2} - 4 \times 576 = 4096$
[From Eqs. (ii)and (iii)]
$\Rightarrow \ \ \ P - Q = 64$ ….(iv)
On solving Eqs. (iii) and (iv), we get
$P = 72,\ Q = 8$
Hence, greater number is 72.