Daily Math Puzzle: 2026-09-23
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2026-09-23
In the ancient ruins, an adventurer discovers a magical flask containing the legendary Elixir of Restoration, which is exactly 3/5 full. During an unexpected skirmish with a band of Goblin raiders, 20% of the elixir *currently in the flask* is tragically spilled. Later, to prepare for a crucial encounter with a formidable dragon, a wise sage adds potent new ingredients, increasing the elixir's volume by 25% *of the flask's total capacity*. What fraction of the flask is now filled with the Elixir of Restoration?
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Solution
73/100 — Let the total capacity of the flask be 'C'.
1. **Initial Amount:** The flask is 3/5 full, so it contains (3/5)C of elixir.
2. **After the Spill:** 20% of the elixir *currently in the flask* is spilled. This means 20% of (3/5)C is lost.
* Amount spilled = 0.20 * (3/5)C = (1/5) * (3/5)C = (3/25)C.
* Amount remaining after spill = (3/5)C - (3/25)C = (15/25)C - (3/25)C = (12/25)C.
3. **After Adding Ingredients:** The sage adds new ingredients, increasing the volume by 25% *of the flask's total capacity*. This means 25% of C is added.
* Amount added = 0.25 * C = (1/4)C.
4. **Final Amount:** Add the amount remaining after the spill to the amount added by the sage.
* Final amount = (12/25)C + (1/4)C
* To add these fractions, find a common denominator, which is 100.
* Final amount = (48/100)C + (25/100)C = (73/100)C.
Therefore, 73/100 of the flask is now filled with the Elixir of Restoration.
Common pitfalls include: applying both percentages to the total capacity (leading to 13/20), applying both percentages to the current amount multiplicatively (leading to 3/5), or performing the operations in the wrong order.
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