Ratio, Proportion, Indices, LogarithmMCQMTP June 24 Series IIQuestion 865 of 305
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The students in three classes are in the ratio 2:3:5\displaystyle 2:3:5. If 40\displaystyle 40 students are increased in each class the ratio changes to 4:5:7\displaystyle 4:5:7. Originally the total number of students was

Options

A180\displaystyle 180
B400\displaystyle 400
C100\displaystyle 100
D200\displaystyle 200
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Correct Answer

✅ Option d — 200\displaystyle 200

All Options:

  • A180\displaystyle 180
  • B400\displaystyle 400
  • C100\displaystyle 100
  • D200\displaystyle 200

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Detailed Solution & Explanation

Let the original number of students in the three classes be 2x\displaystyle 2x, 3x\displaystyle 3x, and 5x\displaystyle 5x respectively.
The original total number of students is:
Total Students=2x+3x+5x=10x\text{Total Students} = 2x + 3x + 5x = 10x
After increasing the number of students in each class by 40\displaystyle 40, the new number of students in each class becomes:
- Class 1: 2x+40\displaystyle 2x + 40
- Class 2: 3x+40\displaystyle 3x + 40
- Class 3: 5x+40\displaystyle 5x + 40
The new ratio is given as 4:5:7\displaystyle 4:5:7. Using the ratio of the first two classes:
2x+403x+40=45\frac{2x + 40}{3x + 40} = \frac{4}{5}
Cross-multiplying to solve for x\displaystyle x:
5(2x+40)=4(3x+40)5(2x + 40) = 4(3x + 40)
10x+200=12x+16010x + 200 = 12x + 160
200−160=12x−10x200 - 160 = 12x - 10x
40=2x  ⟹  x=2040 = 2x \implies x = 20
Let us verify this with the ratio of the second and third classes:
3x+405x+40=3(20)+405(20)+40=100140=57\frac{3x + 40}{5x + 40} = \frac{3(20) + 40}{5(20) + 40} = \frac{100}{140} = \frac{5}{7}
This is consistent with the given ratio. Now, we find the original total number of students:
Original Total=10x=10×20=200\text{Original Total} = 10x = 10 \times 20 = 200
This matches **Option D**.
Hence, **Option D** is the correct answer.

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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