NIMCET 2017 Question Paper with solutions

Let the two number be a and b.
According to the question, we have

2ab

a+b

= 4
and 2A + G2 = 27 [ A =

a+b

2

, G = √ab]

∴ 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 =

18

a

from Eqs, (iv) in Eqs. (iii), we get
a +

18

a

= 9
⇒ a2 - 9a + 18 = 0
⇒ (a + 3) (a - 6) = 0
⇒ a = 3 , 6
∴ b = 6 , 3
∴ Required numbers are 3 and 6.