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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.**View the archive of all weekly problems grouped by curriculum topic*