Ratio, Proportion, Indices, LogarithmMCQMTP March 21Question 851 of 305
All Questions

Which of the numbers are not in proportions?

Options

A6,8,5,7\displaystyle 6,8,5,7
B7,3,14,6\displaystyle 7,3,14,6
C18,27,12,18\displaystyle 18,27,12,18
D8,6,12,9\displaystyle 8,6,12,9
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Correct Answer

✅ Option a — 6,8,5,7\displaystyle 6,8,5,7

All Options:

  • A6,8,5,7\displaystyle 6,8,5,7
  • B7,3,14,6\displaystyle 7,3,14,6
  • C18,27,12,18\displaystyle 18,27,12,18
  • D8,6,12,9\displaystyle 8,6,12,9

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Detailed Solution & Explanation

For four numbers a,b,c,d\displaystyle a, b, c, d to be in proportion, the ratio of the first two numbers must be equal to the ratio of the last two numbers:
ab=cd  ⟹  a⋅d=b⋅c\frac{a}{b} = \frac{c}{d} \implies a \cdot d = b \cdot c
This is known as the product of extremes being equal to the product of means.
Let us test each option:
1. **Option A (6,8,5,7\displaystyle 6, 8, 5, 7)**:
Product of extremes: 6×7=42\displaystyle 6 \times 7 = 42
Product of means: 8×5=40\displaystyle 8 \times 5 = 40
Since 42≠40\displaystyle 42 \neq 40, these numbers are **not in proportion**.
2. **Option B (7,3,14,6\displaystyle 7, 3, 14, 6)**:
Product of extremes: 7×6=42\displaystyle 7 \times 6 = 42
Product of means: 3×14=42\displaystyle 3 \times 14 = 42
Since 42=42\displaystyle 42 = 42, these numbers are in proportion.
3. **Option C (18,27,12,18\displaystyle 18, 27, 12, 18)**:
Product of extremes: 18×18=324\displaystyle 18 \times 18 = 324
Product of means: 27×12=324\displaystyle 27 \times 12 = 324
Since 324=324\displaystyle 324 = 324, these numbers are in proportion.
4. **Option D (8,6,12,9\displaystyle 8, 6, 12, 9)**:
Product of extremes: 8×9=72\displaystyle 8 \times 9 = 72
Product of means: 6×12=72\displaystyle 6 \times 12 = 72
Since 72=72\displaystyle 72 = 72, these numbers are in proportion.
Thus, the numbers in Option A are not in proportion.
Hence, **Option A** 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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