Question

A vessel contains 100 liters of solution having 80 liters of spirit and the remaining is water. If 20 liters of the mixture is taken out from the vessel and replaced by water, then what will be the ratio of spirit to water in the new solution?

• A. 15 : 8
• B. 16 : 9
• C. 17 : 8
• D. 3 : 2

Hint:

Remove components in same ratio as present

Answer 1

The Correct Option is B

Step 1: Determine initial quantities.
Total solution = 100 L.
Spirit = 80 L.
Water = 100 - 80 = 20 L. Step 2: Find amount of spirit and water removed when 20 L mixture is taken out.
Fraction of spirit in mixture = \(\frac{80}{100} = \frac{4}{5}\).
Spirit removed = \(20 \times \frac{4}{5} = 16\) L.
Water removed = \(20 \times \frac{1}{5} = 4\) L. Step 3: Calculate remaining spirit and water after removal.
Remaining spirit = \(80 - 16 = 64\) L.
Remaining water = \(20 - 4 = 16\) L. Step 4: Add 20 L of water.
New water quantity = \(16 + 20 = 36\) L.
Spirit remains 64 L. Step 5: Find the ratio of spirit to water.
Ratio = \(64 : 36\).
Divide both terms by 4: \(16 : 9\).