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?

Answer 1

Hint:Proceed the answer to this question by assuming the current age of Zeba and trying to make a quadratic as per the condition given within the following question. and therefore the roots of that quadratic will give the particular age of Zeba.

Complete step-by-step answer:
Let $x = $ Zeba’s present actual age
In the question it's as long as,
Zeba were younger by \[5\] years than what she really, is write in expression as \[\left( {x - 5} \right)\] years
Square of her age [i.e. square of \[\left( {x - 5} \right)\] ] would are $11$ quite five times her actual age $(x)$
equation is formed as
\[ \Rightarrow {\left( {x - 5} \right)^2} = 11 + 5x\]
( Using ${(a - b)^2} = {a^2} + {b^2} - 2ab$ here, $a = x$and\[b = 5\] )
\[ \Rightarrow {x^2} + 25 - 10x = 11{\text{ }} + {\text{ }}5x\]
On arranging one side and forming equation ,
$
\Rightarrow {x^2} - 15x + 14 = 0 \\
\Rightarrow {x^2} - 14x - x + 14 = 0 \\
\Rightarrow x(x - 14) - 1(x - 14) = 0 \\
\Rightarrow (x - 1)(x - 14) = 0 \\
\Rightarrow x - 1 = 0 \\
\Rightarrow x = 1 \\
and \\
\Rightarrow x - 14 = 0 \\
\Rightarrow x = 14 \\
$
Since her age cannot be $1$ , So it is $14$ .
Zeba’s present actual age $ = 14$ .

Note: In such forms of particular questions, we got two roots from the equation formed by the given condition within the question. Here, sometimes both roots are the right answer and sometimes just one root we select as an accurate answer. It depends on roots whether or not they are satisfying the given condition given within the question or not. If both roots satisfy the given conditions, then both are selected because of the correct answer. For example- within the above question, for $x = 1$ , When Zeba was younger by $5$ years, then her age is expressed as $(x - 5)$ i.e. $(1 - 5) = - 4$ , which could be a negative quantity and Age can’t be negative, hence $x = 1$ can’t be the proper answer.