KnowledgeBoat Logo
|

Mathematics

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

Quadratic Equations

33 Likes

Answer

Let the present age of Mr. Pratap be x years.

After 40 years his age will be (x + 40) years

32 years before his age was (x - 32) years

According to question ,

⇒(x−32)2=(x+40)⇒x2+1024−64x=x+40⇒x2−64x−x+1024−40=0⇒x2−65x+984=0⇒x2−24x−41x+984=0⇒x(x−24)−41(x−24)=0⇒(x−41)(x−24)=0⇒x−41=0 or x−24=0x=41 or x=24\Rightarrow (x - 32)^2 = (x + 40) \\[1em] \Rightarrow x^2 + 1024 - 64x = x + 40 \\[1em] \Rightarrow x^2 - 64x - x + 1024 - 40 = 0 \\[1em] \Rightarrow x^2 - 65x + 984 = 0 \\[1em] \Rightarrow x^2 - 24x - 41x + 984 = 0 \\[1em] \Rightarrow x(x - 24) - 41(x - 24) = 0 \\[1em] \Rightarrow (x - 41)(x - 24) = 0 \\[1em] \Rightarrow x - 41 = 0 \text{ or } x - 24 = 0 \\[1em] x = 41 \text{ or } x = 24

But x ≠ 24 as it is less than 32.

∴ x = 41.

The present age of Mr. Pratap is 41 years.

Answered By

13 Likes

Related Questions