Question

The sum of the ages of Karan and his father Hukum is 100. When Karan is as old as Hukum is now, he will be 5 times as old as his son, Purnendu is now. When Karan is as old as his father, Purnendu will be 8 years older than what Karan is now. Fidn th epresent age of Hukum, Karan and Purnendu.

Answer 1

let the present of Karan's father be x .  
than the age of karan =(100-x)      
{given, karan age + karan's father age = 100}
gap or difference between karan's father and karan's age = x-(100-x)
=x-100+x
=2x-100
after 2x-100 years karan will be as old as his father is now.
his father age is x now. therefore karan's age after 2x-100 years is also x.
that time karan will be 5 times as old as his son, purnendu is now.
let purnendu present age = y
than the equation form = x = 5y
{⇒ y = x/5} ---------------------------------- (equation 1)
when karan is x years old then purnendu will be y+(2x-100) years old and 8 years than karan is now
∴ y +(2x-100) = (100-x) + 8     ----------------(equation 2)
⇒ x/5 + (2x - 100) = 108 - x
⇒ (x+ 10x - 500) / 5 = 108 - x
⇒ x + 10x - 500 = 540 - 5x
⇒ x + 10x + 5x = 540 + 500
⇒ 16x = 1040 
⇒ x = 1040/16
⇒ x = 65
 
∴ karan's father's age (hukum) is 65 years 
   karan's age = 100 - x = 100 - 65 = 35 years
   purnendu's age = x/5 = 65/5 = 13 years

Answer 2

hukums age is 65 years age , Karans is 35 years and perandu's age is 13 years