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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.

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,
$x = \dfrac{{ - b \pm \sqrt {{b^2} - 4ac} }}{{2a}}$