Multiple choice

A vessel is full of a mixture of spirit and water containing 18% spirit. Eight litres of the mixture is drawn and then, the vessel is filled with water. If the present percentage of spirit is 15%, then find the total quantity of mixture in the vessel.

  1. 45 litres

  2. 48 litres

  3. 49 litres

  4. 52 litres

  5. None of these
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Using the formula for replacement: Final concentration = Initial * (1 - x/V)^n. 15 = 18 * (1 - 8/V)^1. 15/18 = (V-8)/V. 5/6 = 1 - 8/V. 8/V = 1/6. V = 48.

AI explanation

When 8 litres are drawn and replaced with water, the remaining spirit is 15/18 of the original amount, meaning 1 minus 15/18 equals 3/18, or 1/6, of the mixture was removed. Since 1/6 of the total capacity is the 8 litres that were drawn, the total quantity of the vessel is 8 times 6, equaling 48 litres.

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