R is a commutative ring and \(|R|=30\). If I is an ideal of R and \(|I|=10\),

Let R be an order 30 commutatie ring, and I be an ideal of R with order 10.

Then \(\displaystyle\frac{{R}}{{I}}\) has order 3 and is thus isomorphic to \(\displaystyle\mathbb{Z}_{{3}}.\)

Since \(\displaystyle\mathbb{Z}_{{3}}\) is field, I must be a maximal ideal.

Hence, proved