Question

Consider three mixtures - the first having water and liquid A in the ratio 1 : 2, the second having water and liquid B in the ratio 1 : 3, and the third having water and liquid C in the ratio 1 : 4. These three mixtures of A, B, and C, respectively, are further mixed in the proportion 4:3:2. Then the resulting mixture has

• A. The same amount of water and liquid B
• B. The same amount of liquids B and C
• C. More water than liquid B
• D. More water than liquid A

Answer 1

The Correct Option is C

The problem involves mixing three solutions and calculating the resulting composition to identify if the resulting mixture has more water than one of its components. Let's break down the solution step by step: 

1. Individual Ratios: For each mixture:
   • First Mixture: Water to Liquid A = 1:2. Assume total parts = 1 + 2 = 3. Therefore, water = 1 part, Liquid A = 2 parts.
   • Second Mixture: Water to Liquid B = 1:3. Total parts = 1 + 3 = 4. Therefore, water = 1 part, Liquid B = 3 parts.
   • Third Mixture: Water to Liquid C = 1:4. Total parts = 1 + 4 = 5. Therefore, water = 1 part, Liquid C = 4 parts.
2. Proportions of Mixing: The mixtures are combined in the ratio 4:3:2. Let's consider the parts of the mixtures:
   • First mixture gets 4 parts, second mixture 3 parts, and third mixture 2 parts.
   • Calculate the contribution of each liquid and water from these proportions.
3. Calculate Contributions in the Final Mixture:
   • Total parts from first mixture = 4. Water = \(\frac{1}{3} \times 4 = \frac{4}{3}\). Liquid A = \(\frac{2}{3} \times 4 = \frac{8}{3}\).
   • Total parts from second mixture = 3. Water = \(\frac{1}{4} \times 3 = \frac{3}{4}\). Liquid B = \(\frac{3}{4} \times 3 = \frac{9}{4}\).
   • Total parts from third mixture = 2. Water = \(\frac{1}{5} \times 2 = \frac{2}{5}\). Liquid C = \(\frac{4}{5} \times 2 = \frac{8}{5}\).
4. Aggregate Water in the Mixture: Total water = \(\frac{4}{3} + \frac{3}{4} + \frac{2}{5}\).
5. Comparing Water to Liquid B: Total Liquid B = \(\frac{9}{4}\). We need to compare this with the calculated water content:
   • To get a common denominator, convert: \(\frac{4}{3} = \frac{80}{60}\), \(\frac{3}{4} = \frac{45}{60}\), \(\frac{2}{5} = \frac{24}{60}\).
   • Therefore, total water = \(\frac{80 + 45 + 24}{60} = \frac{149}{60}\).
   • Liquid B = \(\frac{9}{4} = \frac{135}{60}\).
   • Since \(\frac{149}{60} > \frac{135}{60}\), there is more water than liquid B in the final mixture.

Therefore, the answer is: More water than liquid B.