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The ratio $a : b = 2 :3$ and the ratio $a : c = 3 : 4$. What is the ratio $b : c$?                                                                                                                                                                                                                         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.