Discussion

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 \(= (3 \times 11) = 33.\)

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