Question

    The ratio of two numbers is 3:5. If 9 is subtracted from both, the new ratio becomes 12:23. Determine the original numbers.

    A 27 and 45 Correct Answer Incorrect Answer
    B 36 and 60 Correct Answer Incorrect Answer
    C 33 and 55 Correct Answer Incorrect Answer
    D 30 and 50 Correct Answer Incorrect Answer

    Solution

    Let the numbers be 3x and 5x.  After subtracting 9: (3x - 9)/(5x - 9) = 12/23  Cross-multiplying: 23(3x - 9) = 12(5x - 9)  69x - 207 = 60x - 108  9x = 99  x = 11  Original numbers: 3x = ₹33 and 5x = ₹55  Answer: c) 33 and 55

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