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Answer: $9 : 8$


Using ratio
$a : b$
$2 : 3$ (given)

$a\hspace{2.9mm}:\hspace{2.9mm}c$
$3\hspace{2.9mm}:\hspace{2.9mm}4$ (given)

$a:b:c$
$6:9:8$ (since $3\times2=2\times3=6$)


Using fractions
$$\frac{b}{c} = \frac{a}{c} \times\frac{b}{a}= \frac{3}{4} \times\frac{3}{2} = \frac{9}{8}$$
This problem is taken from the UKMT Mathematical Challenges.
You can find more short problems, arranged by curriculum topic, in our short problems collection.