Question

two number are in ratio 5 is to 6 if 8 is subtracted from each the ratio becomes 4 is to 5 find both the numbers

Answer 1

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

Answer 2

let the number be x and y
x:y=5:6
x/y=5/6
6x=5y
6x-5y=0…………1)
x-8:y-8=4:5
x-8/y-8=4/5
5x-4y=8……………2)
solving 1 and 2
6x-5y=0 [x4]
5x-4y=8 [x5]
or,24x-20y =0
25x-20y =40
___________
sub)x=40
putting x=40 in equation 1
6x40-5y =0
5y=240
y=240/5
y=48
hence x=40 and y=48
To verify the answer just put the value of x and y in equation 1 and 2 only