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Two numbers are in the ratio 3 : 5. If 9 is subtracted from each, the new numbers are in the ratio 12 : 23. Originally, what is the smaller number?
1. 27
2. 33
3. 39
4. 50

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Correct Answer - Option 2 : 33

Let the original numbers be 3x and 5x.

When 9 is subtracted from both numbers :

∴ 23 ⨯ [3x - 9] = 12 ⨯ [5x - 9]

∴ 69x − 207 = 60x − 108

∴ 9x = 99

∴ x = 11

∴ Smaller number = 3x = 3 ⨯ 11 = 33

Hence, ‘33’ is the correct answer.

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