When 30% of one number is subtracted from another number, the second number reduces to its four-fifths. What is the ratio of the first to the second number?

1. 2 : 5

2. 2 : 3

3. 4 : 7

4. cannot be determined

Let the first number be x and the second number be y.

According to question,

⇒ y - 30% of (x) = $\dfrac{4}{5}$y

$\Rightarrow y - \dfrac{30}{100}x = \dfrac{4}{5}y \\[1em] \Rightarrow y - \dfrac{3}{10}x = \dfrac{4}{5}y \\[1em] \Rightarrow y - \dfrac{4}{5}y = \dfrac{3}{10}x \\[1em] \Rightarrow \dfrac{y}{5} = \dfrac{3}{10}x \\[1em] \Rightarrow \dfrac{x}{y} = \dfrac{1}{5} \times \dfrac{10}{3} \\[1em] \Rightarrow \dfrac{x}{y} = \dfrac{10}{15} \\[1em] \Rightarrow \dfrac{x}{y} = \dfrac{2}{3}.$

⇒ x : y = 2 : 3.

Hence, option 2 is the correct option.