Please tell question no.9
​Q9. The ratio of two numbers is $\frac{2}{3}$. If 2 is subtracted from the first and 8 from the second, the ratio becomes the reciprocal of the original ratio. Find the numbers.

x/y = 2/3 ( equation 1)
2 is subtracted from x and 8 from y so it becomes reciprocal then 
x-2/y-8 = 3/2(equation 2)
 
now simplify equation 1
x/y = 2/3
3x = 2y ( cross multiply)
3x -2y = 0
 
equation 2 
x-2/y-8 = 3/2
2x - 4 =3y - 24
2x - 3y = -24 +4
2x - 3y = -20

now subtract  1 from 2

        3x - 2y = 0
        2x - 3y = -20
     (-)   (+)      (+)
________________
x + y = 20
y = 20 - x

substitute y in equation 1 
 3x - 2(20 - x) = 0 
3x - 40 + 2x = 0
3x + 2x = 40
5x = 40 
x = 40/5
x = 8

substitute x = 8 in equation 2
2x - 3y = -20
2(8) - 3y = -20
16 - 3y = -20 
-3y = -20 -16 
-3y = -36
y = -36/-3
y = 12
  
so the no.s are 8 and 12
 
verification  also there
x/y = 8 / 12 which is same as 2/3  ( cancelled by 4)
x - 2 / y - 8 = 3 / 2
8 - 2 / 12 - 8
6 / 4 
3 / 2 ( cancelled by 2)
VERIFIED