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CAT 2024 Slot 2 QA Question 4

Multiple choice (+3 / −1) · Arithmetic · Mixture & Alligation · Try it, then check the answer and solution below.

CAT 2024 Slot 2QAArithmetic • Mixture & AlligationEasy
A vessel contained a certain amount of a solution of acid and water. When 2 litres of water was added to it, the new solution had 50% acid concentration. When 15 litres of acid was further added to this new solution, the final solution had 80% acid concentration. The ratio of water and acid in the original solution was
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Answer and solution

Answer: B) 3:5

📌 Core Concept
This problem involves mixtures and concentrations, where we use the concept of concentration to set up equations based on the amount of acid and water before and after adding more components. The governing formula is:
Concentration=Amount of AcidTotal Solution\text{Concentration} = \frac{\text{Amount of Acid}}{\text{Total Solution}}
🔢 Step-by-Step Solution
1
Define Variables:
Let aa be the original amount of acid in liters.
Let ww be the original amount of water in liters.
2
First Addition (2 litres of water):
Acid remains aa.
Water becomes w+2w + 2.
Total solution becomes a+w+2a + w + 2.
Concentration equation:
aa+w+2=0.5\frac{a}{a + w + 2} = 0.5
3
Solve for aa:
a=0.5(a+w+2)2a=a+w+2a=w+2a = 0.5(a + w + 2) 2a = a + w + 2 a = w + 2
4
Second Addition (15 litres of acid):
Acid becomes a+15a + 15.
Water remains w+2w + 2.
Total solution becomes a+w+17a + w + 17.
Concentration equation:
a+15a+w+17=0.8\frac{a + 15}{a + w + 17} = 0.8
5
Substitute a=w+2a = w + 2 into the second equation:
\frac{(w + 2) + 15}{(w + 2) + w + 17}$ = 0.8 \frac{w +

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