\(N=600-450=150\)

According to the law of radioactive decay,

\(\frac{N}{N_{0}}=\left(\frac{1}{2}\right)^{\frac{t}{T_{1 / 2}}} ;\) where \(N_{0}\) is the number of nuclei initially.

\(\therefore \quad \frac{150}{600}=\left(\frac{1}{2}\right)^{\frac{t}{T_{1 / 2}}} ;\) where \(T_{1 / 2}=\) half life.

or \(\quad\left(\frac{1}{2}\right)^{2}=\left(\frac{1}{2}\right)^{\frac{t}{T_{1 / 2}}}\)

\(\Rightarrow t=2 T_{10}=2 \times 10\) minutes \(=20\) minutes