$\frac{1}{4}$ of a tank holds 135 litres of water. What part of the tank is full if it contains 180 litres of water?

### Concept & Formula This follows the rule of Direct Proportion. The volume of water contained varies directly with the fractional part of the tank that is full. $$\frac{\text{Fraction}_1}{\text{Volume}_1} = \frac{\text{Fraction}_2}{\text{Volume}_2}$$ ### Step-by-Step Solution * **Find the full capacity of the tank:** $$\frac{1}{4} \text{ of Capacity} = 135 \text{ litres}$$ $$\text{Total Capacity} = 135 \times 4 = 540 \text{ litres}$$ * **Calculate the required fraction for 180 litres:** $$\text{Required Fraction} = \frac{\text{Current Volume}}{\text{Total Capacity}} = \frac{180}{540}$$ * **Simplify the fraction:** $$\text{Required Fraction} = \frac{18}{54} = \frac{1}{3}$$ ### Exam Strategy & Shortcut Set up a direct equation to find the solution without computing the total capacity explicitly: $$\text{Required Fraction} = \frac{180}{135} \times \frac{1}{4}$$ Divide 180 and 135 by 45 ($45 \times 4 = 180$, $45 \times 3 = 135$): $$\text{Required Fraction} = \frac{4}{3} \times \frac{1}{4} = \frac{1}{3}$$ ### Common Pitfall Inverting the relationship and computing $\frac{135}{180} \times \frac{1}{4}$, which yields $\frac{3}{16}$ and creates confusion when it doesn't appear in the options list. ### Final Answer **Therefore, the correct answer is \frac{1}{3}.**