NIMCET 2017 Question Paper with solutions

Let the two number be a and b.
According to the question, we have
$\frac{2\mathit{a}\mathit{b}}{\mathit{a}+\mathit{b}}$ = 4
and 2A + ${\mathit{G}}^2$ = 27 [ A = $\frac{\mathit{a}+\mathit{b}}{2}$ , G = $\sqrt{\mathit{a}\mathit{b}}$]

∴ ab = 2 (a + b) ... (i)
and a + b + ab = 27 ... (ii)
⇒ a +b + 2 (a + b) = 27
⇒ 3 (a + b) = 27
⇒ a + b = 9 ... (iii)
From Eqs. (i) and (iii), we have
ab = 18 ... (iv)
Putting, b = $\frac{18}{\mathit{a}}$ from Eqs, (iv) in Eqs. (iii), we get
a + $\frac{18}{\mathit{a}}$ = 9
⇒ ${\mathit{a}}^2$ - 9a + 18 = 0
⇒ (a + 3) (a - 6) = 0
⇒ a = 3 , 6
∴ b = 6 , 3
∴ Required numbers are 3 and 6.