I am a fraction. If you multiply me by two, the sum of me is 54. When you divide my numerator by 4, you get 6. When you divide my denominator by 6, you get 5. What decimal am I?

  • 3
    $\begingroup$ What is the sum of me? $\endgroup$ – Elias Benevedes Mar 8 '15 at 0:47
  • $\begingroup$ The numerator is 24 and the denominator is 30, so 24/30... $\endgroup$ – warspyking Mar 8 '15 at 3:18
  • 2
    $\begingroup$ This might be a bit too easy... $\endgroup$ – CyanogenCX Mar 8 '15 at 4:10

The only possible answer is

$\frac{24}{30}=\frac{4}{5}$ = 0.8,

because if dividing the numerator by 4 gives 6, then the numerator must be 24, while if dividing the denominator by 6 gives 5, then the denominator must be 30.

I don't know what the 54 bit means though. I guess it could mean that $24+30=54$, but why multiply by 2? The best interpretation I can come up with is:

I am $\frac{24}{30}=\frac{12}{15}$, so multiplying 'me' (both parts of me) by 2 gives $\frac{2\times 12}{2\times 15}=\frac{24}{30}$, whose 'sum' (numerator plus denominator) is $24+30=54$.


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