two numbers are in the ratio 3:4 when 7 is added to eachthe ratio becomes 4:5.then the numbers are

3:4
let the numbers be 3x: 4x
​3x + 7              4
---------   =    -------
4x + 7              5

by cross multiplying we get
15x + 35 = 16x + 28
16x -15x = 35 -28
therefore x= 7

the numbers are 
3x= 21 and 4x= 28