1. **State the problem:** The cost of fuel varies directly with the number of liters purchased. Given that 15 liters cost 27, find the cost for 40 liters. 2. **Formula for direct variation:** If $y$ varies directly with $x$, then $y = kx$ where $k$ is the constant of proportionality. 3. **Find the constant $k$:** Using the given values, $27 = k \times 15$. 4. **Solve for $k$:** $$ k = \frac{27}{15} = \frac{\cancel{27}}{\cancel{15}} = \frac{9}{5} $$ 5. **Find the cost for 40 liters:** $$ \text{Cost} = k \times 40 = \frac{9}{5} \times 40 $$ 6. **Simplify:** $$ \frac{9}{5} \times 40 = 9 \times \cancel{\frac{40}{5}} = 9 \times 8 = 72 $$ **Final answer:** The cost for 40 liters is 72.