Question 516265
Let x and y are two numbers


x:y=7:11
x/y=7/11
11x=7y
x=7y/11............(1)


(x+7):(y+7)=2:3
(x+7)/(y+7)=2/3
3(x+7)=2(y+7)
3x+21=2y+14
3x=2y+14-21
3x=2y-7............(2)
Put the value of x in (2) from (1)
3(7y/11)=2y-7
21y/11=2y-7
21y=11*(2y-7)
21y=22y-77
21y-22y=-77
-y=-77
y=77
Put the value of y in (1)

x=7y/11............(1)
x=7(77)/11
x=7*7
x=49



Numbers are 49 and 77



49/77=7/11=7:11
(49+7)/(77+7)=56/84=28/42=14/21=2/3=2:3