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:

$$\eqalign{ & {\text{Let}}\,{\text{the}}\,{\text{number}}\,{\text{be}}\,3x\,{\text{and}}\,5x \cr & {\text{Then}},\,\frac{{3x - 9}}{{5x - 9}} = \frac{{12}}{{23}} \cr & \Rightarrow 23\left( {3x - 9} \right) = 12\left( {5x - 9} \right) \cr & \Rightarrow 9x = 99 \cr & \Rightarrow x = 11 \cr & \therefore {\text{The}}\,{\text{smaller}}\,{\text{number}} \cr & = {3 \times 11} \cr & = 33 \cr} $$