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

Answer: Option C

Let the numbers be 3x and 5x
Then,
$$=\frac{3x-9}{5x-9}=\frac{12}{23}$$
⇒ 23(3x - 9) = 12(5x - 9)
⇒ 69x - 207 = 60x - 108
⇒ 9x = 99
⇒ x = 11
∴ Largest number = 5 × 11 = 55