Two numbers are in the ratio 5 : 8. If 10 is subtracted from each number, the ratio becomes 4 : 7. The numbers are :

1. 80 and 40

2. 50 and 80

3. 25 and 40

4. 40 and 25

Let two numbers be x and y.

Given,

Ratio of two numbers = 5 : 8.

$\Rightarrow \dfrac{x}{y} = \dfrac{5}{8} \\[1em] \Rightarrow x = \dfrac{5}{8}y \space …..(1)$

Given,

If 10 is subtracted from each number, the ratio becomes 4 : 7.

$\Rightarrow \dfrac{x - 10}{y - 10} = \dfrac{4}{7} \\[1em] \Rightarrow 7(x - 10) = 4(y - 10) \\[1em] \Rightarrow 7x - 70 = 4y - 40$

Substituting value of x from equation (1), in above equation we get :

$\Rightarrow 7 \times \dfrac{5}{8}y - 70 = 4y - 40 \\[1em] \Rightarrow \dfrac{35y}{8} - 70 = 4y - 40 \\[1em] \Rightarrow \dfrac{35y}{8} - 4y = 70 - 40 \\[1em] \Rightarrow \dfrac{35y - 32y}{8} = 30 \\[1em] \Rightarrow \dfrac{3y}{8} = 30 \\[1em] \Rightarrow y = \dfrac{30 \times 8}{3} \\[1em] \Rightarrow y = 80. \\[1em] \Rightarrow x = \dfrac{5}{8}y \\[1em] \Rightarrow x = \dfrac{5}{8} \times 80 = 50.$

Numbers = 50 and 80.

Hence, Option 2 is the correct option.