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'Weekly Problem 44 - 2013' printed from

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Two thirds of five sixths of a number $X$ is the same as three quarters of four fifths of a number $Y$.

What is the value of $\frac{X}{Y}$ as a fraction in its lowest terms?
If you liked this problem, here is an NRICH task which challenges you to use similar mathematical ideas.  

This problem is taken from the UKMT Mathematical Challenges.

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