# 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.

Let us consider the two numbers are x and y

Given:

x/y = 5/6

x × 6 = y × 5

6x – 5y = 0………………..(1)

If 8 is subtracted from each of the numbers then the ratio is 4:5.

$$\begin{array}{l}\frac{x-8}{y-8}= \frac{4}{5}\end{array}$$

⇒ 5x – 40 = 4y – 32

Then the equation is

5x – 4y = 8……………….(2)

From equation (1)

x = 5y/6

Substituting value of x in equation (2)

5(5y/6) – 4y = 8

y = 48

Substitute the value of y in equation (1) we get

6x – 5(48) = 0

6x = 240

x = 40

Therefore the numbers are 40 and 48.