Average, Mixture and Alligation Question 1 - CAT 2020
Two alcohol solutions, A and B, are mixed in the proportion 1 : 3 by volume. The volume of the mixture is then doubled by adding solution A such that the resulting mixture has 72% alcohol. If solution A has 60% alcohol, then the percentage of alcohol in solution B is:
Step-by-Step Explanation
Let us break this down into a two-stage alligation framework.
- Stage 1 (Doubling the Volume):
The initial mixture (let its concentration be Xₘᵢₓ) is doubled by adding an equal volume of pure solution A (60% alcohol). This implies a blending ratio of exactly 1 : 1. The resulting mix concentration is 72%.
(Xₘᵢₓ + 60) / 2 = 72 ⟹ Xₘᵢₓ + 60 = 144 ⟹ Xₘᵢₓ = 84%
- Stage 2 (Finding Solution B):
The initial mixture was formed by blending solution A (60%) and solution B (let its concentration be Xᴮ) in a 1 : 3 volume ratio to achieve this 84% benchmark.
(1 × 60 + 3 × Xᴮ) / (1 + 3) = 84
60 + 3Xᴮ = 84 × 4
60 + 3Xᴮ = 336
3Xᴮ = 276 ⟹ Xᴮ = 92%
The percentage of alcohol in solution B is 92%.
Correct Option: C
💡 FundaMakers Tip:
Work backward from the final state. When a problem mentions that the volume of a mixture is doubled by adding a single component, it is a structural shortcut revealing a perfect 1 : 1 ratio. Finding the intermediate mixture's concentration (84%) via a quick mid-point calculation saves you from writing complex multi-variable tracking equations.