**Let the two numbers be x, y**

**\(\frac{x}{y}=\frac{5}{6}\)**

⇒ 6x = 5y

**6x – 5y = 0 … (1) **

**\(\frac{x-8}{y-8}=\frac{4}{5}\)**

⇒ 5(x – 8) = 4(y – 8)

5x – 40 = 4y – 32

5x – 4y = 40 – 32

**5x – 4y = 8 … (2)**

**Substitute y = 48 in (1)**

6x – 5(48) = 0

6x – 240 = 0

6x = 240

**x = \(\frac{240}{6}\) = 40**

\(\frac{x}{y}=\frac{40}{48}=\frac{5}{6}\)

**∴ The numbers are in the ratio 5 : 6**