Ratio, Proportion, Indices, LogarithmMCQPYQ Dec 21Question 802 of 302
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In a department, the number of males and females are in the ratio $3:2.If\displaystyle . If2malesand\displaystyle males and5$ females join the department, then the ratio becomes $2:1$. Initially, the number of females in the department is

Select Your Answer (Keyboard: A, B, C, D)
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Correct Answer

✅ Option b — 8\displaystyle 8

All Options:

  • A9\displaystyle 9
  • B8\displaystyle 8
  • C3\displaystyle 3
  • D6\displaystyle 6

Detailed Solution & Explanation

Let the initial number of males and females in the department be $3x\displaystyle and $2x respectively.
When 2\displaystyle 2 males and 5\displaystyle 5 females join, the new counts are $3x + 2\displaystyle and $2x + 5 respectively.
The new ratio is $1 : 1$, which means the counts are equal:
3x+2=2x+53x + 2 = 2x + 5
3x−2x=5−2  ⟹  x=33x - 2x = 5 - 2 \implies x = 3
Initially, the number of females is:
Females=2x=2(3)=6Females=2x=2\displaystyle \text{Females} = 2x = 2(3) = 6

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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