Question

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 present in the tank?

• A. \(35%\)
• B. \(37%\)
• C. \(40%\)
• D. \(37.5%\)
• E. \(32.5%\)

Answer 1

The Correct Option is D

Concept: This is a
repeated replacement problem:

• Each time half the mixture is removed
• Remaining quantity keeps halving

Step 1: Initial fill.
Tank full of A = 1
Step 2: After first replacement (add B).
Remaining A = \( \frac{1}{2} \)
Step 3: After second replacement (add A).
Remaining previous mixture = \( \frac{1}{2} \times \frac{1}{2} = \frac{1}{4} \) New A added = \( \frac{1}{2} \) Total A: \[ \frac{1}{4} + \frac{1}{2} = \frac{3}{4} \]
Step 4: After third replacement (add B).
Remaining A: \[ \frac{3}{4} \times \frac{1}{2} = \frac{3}{8} \]
Step 5: Final percentage.
\[ \frac{3}{8} = 37.5% \]
Step 6: Option analysis.

• (A) 35%: Incorrect $\times$
• (B) 37%: Approximation $\times$
• (C) 40%: Incorrect $\times$
• (D) 37.5%: Correct \checkmark
• (E) 32.5%: Incorrect $\times$

Conclusion:
Thus, the correct answer is
Option (D).