#### 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?

14

Solution

Let zeba’s current age = x

According to question
$\\(x-5)^{2}=11+5x\\ x^{2}+25-10=11+5x\;\;\;\;\;\;\;\(using \;\;(a-b)^{2}=a^{2}+b^{2}-2ab)\\ x^{2}+25-10x-11-5x=0\\ x^{2}-15x+14=0\\ x^{2}-14x-x+14=0\\ x(x-14)-1(x-14)=0\\ (x-14)(x-1)\\$

x = 14

we can’t take 1 because if we take 5 years younger of 1 then it is equal to – 4 and age cannot be negative.

Hence x = 14 i.e., the age of zeba is 14 years