If the ratio between two numbers …

Let 1st number (numerator) be x

let 2nd number (denominator) be y

they are in ratio so theri ratio = x / y

as per sum

1 condition = x / y = 5 / 6

6x = 5y

6x - 5y = 0 ----- 1

2 condition = x-8 / y-8 = 4 / 5

5x - 4y = -32 + 40

5x - 4y = 8 ------- 2

By substitution method

x = 5y / 6 (from 1)

putting value of x in equation 2

5 ( 5y / 6 ) - 4y = 8

25y - 24y / 6 = 8

25y - 24y = 8 X 6

y = 48

putting value of y in equation 1

6x - 5(48) = 0

6x = 240

x = 240 / 6

x = 40

Value of x = 40

Value of y = 48

Let the two no be x and y
therefore x / y = 5 / 6
6 * x = 5 * y
6 * x - 5 * y = 0             * 5
    30 * x -     25 * y = 0 ..................(i)
also (x - 8)/(y - 8) = 4 / 5
5 * x - 40 = 4 * y - 32
5 * x - 4 * y - 8 = 0                 *6
30 * x - 24 * y - 48 = 0 .....................(ii)
subtracting  (i) from (ii)
y - 48 = 0
y = 48
putting y = 48 in x/y = 5/6
x/48 = 5/6
x = 5 * 48 / 6
x = 5 * 8
x = 40
therefore the two numbers are 40 and 48