Question

Find the present age of a man if his age 40 years hence will become equal to the square of what his age was 32 years ago

Answer 1

Solution :-

Let the present age of a man be x years.

According to the question,

=> x + 40 = (x - 32)²

=> x + 40 = x² - 64x + 1024

=> x² - 64x - x + 1024 - 40 = 0

=> x² - 65x + 984 = 0

=> x² - 41x - 24x + 984 = 0

=> x(x - 41) - 24(x - 41) = 0

=> (x - 41) (x - 24) = 0

=> x = 41 or x = 24

∴ x ≠ 24 years (Because if we find their age 32 years ago then the age will be negative and we know that age is always taken positive)

Hence,

Age of a man = 41 years

Answer 2

Hola!!

Here is your answer :-

Let the present age of the man be x years.

Then,
A/q_⬅

$x + 40 = {(x - 32)}^{2} \\ \\using \: {(a - b)}^{2} \\ \\ x + 40 = {x}^{2} - 64x + 1024 \\ \\ {x}^{2} - 64x + 1024 = x + 40 \\ \\ {x}^{2} - 64x + 1024 - x - 40 = 0 \\ \\ {x}^{2} - 65x + 984 = 0 \\ \\ {x}^{2} - 41x - 24x + 984 = 0 \\ \\ x(x - 41) - 24(x - 41) \\ \\ (x - 41)( x - 24) = 0$


So,

x =24 and x =41..

If we take 24 years as his present age then it will become negative, which is not possible.

So, the present age of the man is 41 years....

Thanks!