Question

Raj is 6 years older than diya.one half of raj’s age exceeds one -third of diya's age by 4 years.find their ages

Answer 1

let the age of diya be x,

Age of raj be x+6 

_________________
Now,

one half of raj's age =  $\frac{x+6}{2}$'

one third of diya's age = $\frac{x}{3}$

ATQ,

$\frac{x+6}{2} = \frac{x}{3} + 4$


$\frac{x+6}{2} = \frac{x+ 12 }{3}$


cross multiply

3(x+6) = 2(x+12)

3x + 18 = 2x +24 

3x-2x = 24-18

x = 6 years


Now,

age of diya is 6 years'

and 

age of raj is 6+6 = 12 years


i hope this will help you


-by ABHAY

Answer 2

Hi,

Please see the attached file!

Thanks