Question

Two numbers are in the ratio 5:6. If 8 is subtracted from each of the numbers , the ratio becomes 4:5 find 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

Answer:

The numbers are 40 and 48

Step-by-step explanation:

Let two numbers be 5x and 6x

According to question,

(5x-8):(6x-8)= 4:5

so, (5x-8)/(6x-8)= 4/5

By Cross multiplication,

(5x-8)×5=(6x-8)×4

25x-40=24x-32

25x-24x=40-32

x=8

Therefore numbers are (5×8)= 40 and (6×8)= 48

Here I applied here all basic rules of ratio.