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 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