Two numbers are in the ratio 5 : 7. If 8 is subtracted from each, the ratio becomes 3 : 5. Find the numbers.

Let the numbers be 5x and 7x.

Given,

If 8 is subtracted from each, the ratio becomes 3 : 5.

$\Rightarrow \dfrac{5x - 8}{7x - 8} = \dfrac{3}{5} \\[1em] \Rightarrow (5x - 8) \times 5 = (7x - 8) \times 3 \\[1em] \Rightarrow 25x - 40 = 21x - 24\\[1em] \Rightarrow 25x - 21x = 40 - 24 \\[1em] \Rightarrow 4x = 16 \\[1em] \Rightarrow x = \dfrac{16}{4} \\[1em] \Rightarrow x = 4.$

The two numbers are 5x and 7x

= 5 × 4, 7 × 4

= 20, 28.

Hence, the numbers are 20 and 28.