1. **Stating the problem:** Mr Lim saved 30000 for 5 years and received interest of 6000. Interest $I$ varies directly as principal $P$ and time $t$. Find the interest if he saves for 8 years. 2. **Formula and explanation:** Since $I$ varies directly as $P$ and $t$, we write: $$I = kPt$$ where $k$ is the constant of proportionality. 3. **Find constant $k$ using given data:** Given $I=6000$, $P=30000$, $t=5$, substitute: $$6000 = k \times 30000 \times 5$$ 4. **Solve for $k$:** $$k = \frac{6000}{30000 \times 5} = \frac{6000}{150000}$$ $$k = 0.04$$ 5. **Calculate interest for $t=8$ years:** $$I = 0.04 \times 30000 \times 8$$ $$I = 0.04 \times 240000$$ $$I = 9600$$ 6. **Calculate total savings after 8 years:** Total savings = Principal + Interest $$= 30000 + 9600 = 39600$$ **Final answer:** Mr Lim's total savings after 8 years is 39600.