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Forty years hence, Mr. Pratap’s age will be the square of what it was $32$ years ago. Find the present age.

Last updated date: 17th Mar 2023
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Hint:If it says $x$ years hence it would mean $x$ years from this year. We have to find the age of Mr. Pratap, his present age is to be found, this means that we have to make a mathematical equation out of this statement, we will take his present age to be $x$ the question then says that the age $32$ years ago will be the square root of Mr. Pratap’s age $40$ years after. This simply means we can form an equation and solve this. The equation would be a quadratic one as squares are involved so either we can solve by the factorization or we can solve by the quadratic method.

Complete step by step answer:
We will take Mr. Pratap's current age to be $x$ . This means that his age forty years from today will be $x + 40$, the age $32$ years ago was $x - 32$. The question then says age after the $40$ years will be the square of the age $32$ years ago.So our equation becomes,
${(x - 32)^2} = x + 40$
\[ \Rightarrow {x^2} + 1024 - 64x = x + 40\]
\[ \Rightarrow {x^2} - 65x + 984 = 0\]
The equation is a quadratic equation, we will now solve it by factorization,
${x^2} - 24x - 41x + 984 = 0$
$ \Rightarrow x(x - 24) - 41(x - 24) = 0$
Upon solving the equation we get,
$x = 24$, and,
$\therefore x = 41$,
Since $24$ cannot be our age as he is more than $32$ years of age, we can say that his current age is $41$ years.

Note:The equation above is a quadratic equation, had it not been able to be solved by the factorization method we will then use the quadratic formula. The quadratic equation of the form,
$a{x^2} + bx + c = 0$, have the solution of the form,
$x = \dfrac{{ - b \pm \sqrt {{b^2} - 4ac} }}{{2a}}$