Question

The ages of Aman and Arun are in the ratio 5:7. Four years later the sum of their ages will be 56 years. What are their present ages

Answer 1

Aman's age = 20, Arun's age = 28

Explanation:

Let
`x` = Aman's age

Let
`y` = Arun's age

- - - -

`x+4+y+4=56` (Sum of their age is 56 after 4 years in the future)

`x+y+8=56`

`x+y=48`

`(x)/(y) = (5)/(7)` (Ages are in the ratio 5:7)

`x=(5)/(7)y`

Now, we can use substitution to find for Arun's age:

`x+y=48`

`(5)/(7)y+y=48`

`(12)/(7)y=48`

`y=28`

∴ Arun is
`28`

To find for Aman's age, we can use substitution:

`x+y=48`

`x+28=48`

`x=20`

∴ Aman is 20

Hope this helps :)