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Two numbers are in the ratio 3:5. If 9 is subtracted from each number, the ratio becomes 12:23. The smaller number is?
  1. 32
  2. 33
  3. 31
  4. None of these
Explanation

Let the smaller number be 3x and the larger number be 5x, since their ratio is 3:5.

When 9 is subtracted from each number, the new numbers are 3x - 9 and 5x - 9.

The ratio of these new numbers is 12:23, so we can set up the equation:

(3x - 9) / (5x - 9) = 12/23

Cross-multiplying and simplifying the equation, we get:

69x - 207 = 60x - 108

Solving for x, we get:

9x = 99

x = 11

So, the smaller number is 3x = 3(11) = 33.

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