Discussion
If the numerator of a fraction is increased by 300% and the denominator is increased by 400%, the resultant fraction is \(\frac{16}{25}\). What was the original fraction ?
Answer: C
The original fraction was \(\frac{4}{5}\).
Increasing by 300% multiplies the numerator by 4, and increasing by 400% multiplies the denominator by 5. If the fraction was \(\frac{x}{y}\):
\[ \begin{aligned} \frac{4x}{5y} &= \frac{16}{25} \\ \frac{x}{y} &= \frac{16}{25} \times \frac{5}{4} = \frac{4}{5} \end{aligned} \]
Check: \(\frac{4 \times 4}{5 \times 5} = \frac{16}{25}\). The common slip is to multiply by 3 and 4 instead of 4 and 5, which treats a 300% increase as tripling.
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