From a 64-liter container of pure spirit, 8 liters are removed and replaced by water. This operation is performed a total of thre…

Question

From a 64-liter container of pure spirit, 8 liters are removed and replaced by water. This operation is performed a total of three times. What is the final quantity of spirit remaining in the container?

1. A. 34.34 liters
2. B. 36.45 liters
3. C. 38.62 liters
4. D. 42.88 liters (Correct answer)

Correct Answer

Option D — 42.88 liters

Detailed Solution & Explanation

The correct answer is 42.88 liters.

Key Points

• For repeated removal and replacement, the quantity of the original liquid remaining is:
  • Final = Initial × (1 − x/T)ⁿ, where x is removed each time from total T, over n operations.
• Substituting: 64 × (1 − 8/64)³ = 64 × (7/8)³.
• (7/8)³ = 343/512, so 64 × 343/512 = 42.875 ≈ 42.88 litres.

Additional Information

• The key insight is that each operation removes the same fraction of whatever spirit remains, not the same quantity — which is why the result is a geometric decay rather than a linear one.
• After three operations the spirit is 343/512 of the original, roughly 67%, so the water content is about 33%.
• The same formula covers milk-and-water replacement, alcohol dilution and any repeated-substitution problem; the only care needed is that x and T share units.

प्रश्न (हिन्दी में)

शुद्ध स्पिरिट के 64 लीटर के कंटेनर से 8 लीटर निकाल कर उसकी जगह पानी डाला जाता है। यह प्रक्रिया कुल तीन बार की जाती है। कंटेनर में बची हुई स्पिरिट की अंतिम मात्रा क्या है?

1. A. 34.34 लीटर
2. B. 36.45 लीटर
3. C. 38.62 लीटर
4. D. 42.88 लीटर