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?

A. 40

B. 45

C. 55

D. 60

Answer: Option C

Solution(By Examveda Team)

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