Kiran is 24 years older than Rakesh. 10 years back Kiran’s age was five times the age of Rakesh. Find their ages.

Let the age of Kiran at Present be x years. 

Then Rakesh’s present age is (x - 24) years 

10 years ago, the age of Kiran = (x - 10) years and the age of Rakesh = (x - 24 - 10) or (x - 34)years 

According to the question, 10 years ago, Kiran’s age is equal to 5 times the age of Rakesh 

∴ $$x-10=5(x-34)$$ 

$$\Rightarrow x-10=5x-170$$ 

$$\Rightarrow x-5x=-170+10$$ 

$$\Rightarrow -4x=-160$$ 

$$\Rightarrow x=$$ $$\frac{-160}{-4}$$ 

$$\Rightarrow x=40$$ 

Hence, Kiran’s age = x = 40 years 

Rakesh’s  age = x - 24 = 40 - 24 = 16 years.