ThinkCAT Logo
ThinkCAT
Sign up
QuestionsMocksResourcesAnalytics

CAT 2025 Slot 3 QA Question 2

Type-in-the-answer (no negative marking) · Arithmetic · Mixture & Alligation · Try it, then check the answer and solution below.

CAT 2025 Slot 3QAArithmetic • Mixture & AlligationModerate
Vessels A and B contain 60 litres of alcohol and 60 litres of water, respectively. A certain volume is taken out from A and poured into B. After stirring, the same volume is taken out from B and poured into A. If the resultant ratio of alcohol and water in A is 15 : 4, then the volume, in litres, initially taken out from A is
TITA Answer:
Practice More Questions
Answer and solution

Answer: 16

📌 Core Concept
The problem involves mixtures and alligation, where we need to track the concentration of alcohol and water after transferring volumes between two vessels. The key concept is to use the concentration of the mixture after each transfer to determine the volume taken out.
🔢 Step-by-Step Solution
1
Define Variables:
Let xx be the volume taken out from vessel A.
2
First Transfer:
xx liters of alcohol are taken from A and poured into B.
Vessel B now has 60 liters of water and xx liters of alcohol, making the total volume 60+x60 + x liters.
3
Concentration in B:
The concentration of alcohol in B is x60+x\frac{x}{60 + x}$.
4
Second Transfer:
xx liters are taken from B and poured back into A.
The amount of alcohol in this xx liters is x260+x\frac{x^2}{60 + x}$.
The amount of water in this xx liters is 60x60+x\frac{60x}{60 + x}$.
5
Final Mixture in A:
Alcohol in A: 60−x+x260+x60 - x + \frac{x^2}{60 + x}.
Water in A: 60x60+x\frac{60x}{60 + x}.
6
Set Up the Ratio:
The ratio of alcohol to water in A is given as 15:4.
60−x+x260+x60x60+x=154\frac{60 - x + \frac{x^2}{60 + x}}{\frac{60x}{60 + x}} = \frac{15}{4}
7
Simplify the Numerator:
60−x+x260+x=(60−x)(60+x)+x260+x=3600−x2+x260+x=360060+x60 - x + \frac{x^2}{60 + x} = \frac{(60 - x)(60 + x) + x^2}{60 + x} = \frac{3600 - x^2 + x^2}{60 + x} = \frac{3600}{60 + x}
8
Simplify the Ratio:
360060+x60x60+x=360060x=60x=154\frac{\frac{3600}{60 + x}}{\frac{60x}{60 + x}} = \frac{3600}{60x} = \frac{60}{x} = \frac{15}{4}
9
Solve for xx:
60x=154  ⟹  60×4=15x  ⟹  240=15x  ⟹  x=16\frac{60}{x} = \frac{15}{4} \implies 60 \times 4 = 15x \implies 240 = 15x \implies x = 16
⚡ 30-Second Shortcut
Recognize that the concentration of alcohol in vessel B after the first transfer is x60+x\frac{x}{60 + x}$.
Use the ratio of alcohol to water in

Keep going

Related Mixture & Alligation questions