An empty fuel tank of a car was filled with A type petrol. When the tank was half-empty, it was filled with B type petrol. Again when the tank was half-empty, it was filled with A type petrol. When the tank was half-empty again, it was filled with B type petrol. What is the percentage of A type petrol at present in the tank?

### Concept & Logic This problem requires tracking the sequential dilution and reinforcement of a mixture. Because the tank is always emptied by half and refilled to full, we can trace the remaining quantities of **Type A** petrol through each specific cycle of halving and adding. ### Step-by-Step Solution * **Given:** * Let the full tank capacity be $100$ units. * **Calculation (Cycle by Cycle):** * **Initial State:** Tank is filled with A. * Contents: $100$ A. * **Step 1:** Tank becomes half-empty ($50$ units remain), filled with B ($+50$ B). * Contents: $50$ A, $50$ B. (Mixture is now $50\%$ A). * **Step 2:** Tank becomes half-empty (halving the existing mixture leaves $25$ A, $25$ B), filled with A ($+50$ A). * Contents: $25 + 50 = 75$ A, $25$ B. (Mixture is now $75\%$ A). * **Step 3:** Tank becomes half-empty (halving the existing mixture leaves $37.5$ A, $12.5$ B), filled with B ($+50$ B). * Contents: $37.5$ A, $12.5 + 50 = 62.5$ B. * The question asks for the final percentage of A type petrol. * Final amount of A = $37.5$ units out of $100$ units total = $37.5\%$. ### Exam Strategy & Shortcut **Fraction Tracking Method:** Track only the fraction of Type A fuel at each stage. Start = $1$. After Step 1 (Half A remains) = $\frac{1}{2}$. After Step 2 (Half remains, plus full half added) = $\frac{1}{2}(\frac{1}{2}) + \frac{1}{2} = \frac{1}{4} + \frac{2}{4} = \frac{3}{4}$. After Step 3 (Half remains, no A added) = $\frac{1}{2}(\frac{3}{4}) = \frac{3}{8}$. Convert fraction to percentage: $\frac{3}{8} = 37.5\%$. This avoids tracking both A and B entirely! ### Common Pitfall A common mistake is losing track of which fuel type is being added during which step, or forgetting that "halving" the tank halves *both* fuel types proportionally. Proceed systematically step-by-step or use the fractional shortcut to avoid getting lost in the numbers. ### Final Answer **Therefore, the correct answer is 37.5%.**