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Answer: $\frac{27}{25}$
$$ \frac{2}{3} \times \frac{5}{6} \times X = \frac{3}{4} \times \frac{4}{5} \times Y$$ $$ \frac{5X}{9} = \frac{3Y}{5}$$ $$ 25X = 27Y$$ $$ \frac{X}{Y} = \frac{27}{25}$$
Fractions of Fractions
Age 14 to 16
ShortChallenge Level 
Answer: $\frac{27}{25}$
$$ \frac{2}{3} \times \frac{5}{6} \times X = \frac{3}{4} \times \frac{4}{5} \times Y$$ $$ \frac{5X}{9} = \frac{3Y}{5}$$ $$ 25X = 27Y$$ $$ \frac{X}{Y} = \frac{27}{25}$$
This problem is taken from the UKMT Mathematical Challenges.
You can find more short problems, arranged by curriculum topic, in our short problems collection.
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