Ratio, Proportion, Indices, LogarithmMCQPYQ July 21Question 799 of 305
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A vessel contained a solution of acid and water in which water was 64%\displaystyle 64\%. Four liters of the solution were taken out of the vessel and the same quantity of water was added. If the resulting solution contains 30%\displaystyle 30\% acid, the quantity (in liters) of the solution, in the beginning in the vessel, was

Options

A12\displaystyle 12
B36\displaystyle 36
C24\displaystyle 24
D2\displaystyle 2
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Correct Answer

✅ Option c — 24\displaystyle 24

All Options:

  • A12\displaystyle 12
  • B36\displaystyle 36
  • C24\displaystyle 24
  • D2\displaystyle 2

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Detailed Solution & Explanation

Let the initial quantity of the solution in the vessel be V\displaystyle V liters.
The initial water concentration is 64%\displaystyle 64\%, meaning the acid concentration is 100%−64%=36%\displaystyle 100\% - 64\% = 36\%.
When 4\displaystyle 4 liters of the solution are removed, the remaining volume is V−4\displaystyle V - 4 liters, which still contains 36%\displaystyle 36\% acid.
The amount of acid remains unchanged when 4\displaystyle 4 liters of pure water are added to the mixture.
The new acid concentration is 30%\displaystyle 30\% in the final volume of V\displaystyle V liters:
Acid in remaining solution=Acid in final solution\text{Acid in remaining solution} = \text{Acid in final solution}
36%×(V−4)=30%×V36\% \times (V - 4) = 30\% \times V
0.36(V−4)=0.30V0.36(V - 4) = 0.30V
0.36V−1.44=0.30V0.36V - 1.44 = 0.30V
0.06V=1.44  ⟹  V=24 liters0.06V = 1.44 \implies V = 24 \text{ liters}

About This Chapter: Ratio, Proportion, Indices, Logarithm

Paper

Paper 3: Quantitative Aptitude

Weightage

5-7 Marks

Key Topics

Ratio, Proportion, Indices, Logarithms

This chapter covers Ratio, Proportion, Indices, Logarithms and is part of Paper 3: Quantitative Aptitude in the CA Foundation exam.

View Official ICAI Syllabus

Exam Strategy Tip

This topic carries 5-7 Marks weightage. Focus on understanding core concepts rather than memorizing.

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