Two number are in the ratio \(3 : 5.\) If \(9\) is subtracted from each, the new numbers are in the ratio \(12 : 23.\) The smaller number is:
Answer: B
Let the numbers be \(3x\) and \(5x.\)
Then, \(\frac{3x - 9}{5x - 9} = \frac{12}{23}\)
\(\Rightarrow 23(3x - 9) = 12(5x - 9)\)
\(\Rightarrow 9x = 99\)
\(\Rightarrow x = 11.\)
\(\therefore\) The smaller number \(= (3 \times 11) = 33.\)