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?

Â

If you liked this problem, here is an NRICH task which challenges you to use similar mathematical ideas. Â

This problem is taken from the UKMT Mathematical Challenges.

You can find more short problems, arranged by curriculum topic, in our short problems collection.