Two numbers are in the ratio of 3 : 5. If 9 is subtracted from each, they are in the ratio of 12 : 23. The larger number is :

1. 40

2. 45

3. 55

4. 60

Given,

Let the two numbers be 3k and 5k.

After subtracting 9 from each number, the ratio changes to 12 : 23.

$\therefore \dfrac{3k - 9}{5k - 9} = \dfrac{12}{23} \\[1em] \Rightarrow 23(3k - 9) = 12(5k - 9) \\[1em] \Rightarrow 69k - 207 = 60k - 108 \\[1em] \Rightarrow 69k - 60k = 207 - 108 \\[1em] \Rightarrow 9k = 99 \\[1em] \Rightarrow k = \dfrac{99}{9} \\[1em] \Rightarrow k = 11.$

The larger number = 5k = 5 × 11 = 55.

Hence, option 3 is the correct option.