If Zeba were younger by 5 years than what she . . .

Question : If Zeba were younger by 5 years than what she really is, then the square of her age (in years) would have been 11 more than five times her actual age. What is her age now?

Doubt by Radhika

Solution : 

Let the present age of Zeba be x years.

Age of Zeba five years ago = (x-5) years

ATQ

(x-5)²=11+5x

x²-10x+25=11+5x

x²-10x-5x+25-11=0
x²-15x+14=0

x²-(14+1)x+14=0

x²-14x-x+14=0
x(x-14)-1(x-14)=0
(x-1)(x-14)=0
(x-1)=0 OR (x-14)=0
x=1 OR x=14

x≠1

[∵ Age of Zeba five year ago can't be -ve]

Hence, x=14

So, the present of Zeba must be 14 years.