Question : Two numbers are in the ratio of 3 : 5. If 9 is subtracted from each, then they are in the ratio of 12 : 23. Find the numbers.
Option 1: 15 and 28
Option 2: 36 and 115
Option 3: 33 and 55
Option 4: 60 and 69
Correct Answer: 33 and 55
Solution : Let the numbers be $3x$ and $5x$. According to the question, $\frac{3x-9}{5x-9}=\frac{12}{23}$ $⇒69x -207 = 60x-108$ $⇒9x = 99$ $⇒x =11$ Thus, the numbers are 33 and 55. The correct answer is 33 and 55.
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