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1. 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:

A. 27

B. 33

C. 49

D. 55

Solution:

\begin{aligned} Let the number be 3 x and 5 x \\ Then, \frac{3 x - 9}{5 x - 9} = \frac{12}{23} \\ \Rightarrow 23 (3 x - 9) = 12 (5 x - 9) \\ \Rightarrow 9 x = 99 \\ \Rightarrow x = 11 \\ ∴ The smaller number \\ = 3 \times 11 \\ = 33 \end{aligned}

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