Two numbers are such that the ratio between them is 3:5. If each is increased by 10, the ratio between the new numbers so formed is 5:7. Find the original numbers.

Explanation

Given:
Ration between two numbers is `3:5`.
If each number is increased by `10` the ratio becomes `5:7`.
Now,
Let the two numbers be `3x` and `5x`.
According to question,
`3x+10:5x+10=5:7`
`(3x+10)/(5x+10)=5/7`
`7(3x+10)=5(5x+10)`
`21x+70=25x+50`
`70-50=25x-21x`
`4x=20`
`x=20/4`
`x=5`
Since the numbers assumed were `3x` and `5x`, then the actual values of the numbers will be:
`3x=3xx5=15`
`5x=5xx5=25`
Hence, the two numbers are `15` and `25`.