# 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?

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Given:

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 5 times her actual age.

To do:

We have to find her present age.

Solution:

Let the present age of Zeba be $x$ years.

This implies,

Age of Zeba if she was 5 years younger$=x-5$ years

According to the question,

$(x-5)^2=5x+11$

$x^2-10x+25=5x+11$

$x^2-10x-5x+25-11=0$

$x^2-15x+14=0$

Solving for $x$ by factorization method, we get,

$x^2-14x-x+14=0$

$x(x-14)-1(x-14)=0$

$(x-14)(x-1)=0$

$x-14=0$ or $x-1=0$

$x=14$ or $x=1$

Zeba\'s age cannot be $1$ year. Therefore, the value of $x$ is $14$.

$x-5=14-5=9$

The present age of Zeba is $14$ years.

Updated on 10-Oct-2022 13:27:26