Two numbers are in the ratio 3:5. If 9 is subtracted from each number, the ratio becomes 12:23. The smaller number is?
- 32
- 33
- 31
- 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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