Ratio, Proportion, Indices, LogarithmMCQPYQ Nov 19Question 791 of 305
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The ratio of two numbers are 3:4\displaystyle 3:4. The difference of their squares is 28\displaystyle 28 greater is:

Options

A8\displaystyle 8
B12\displaystyle 12
C24\displaystyle 24
D64\displaystyle 64
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Correct Answer

✅ Option b — 12\displaystyle 12

All Options:

  • A8\displaystyle 8
  • B12\displaystyle 12
  • C24\displaystyle 24
  • D64\displaystyle 64

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Detailed Solution & Explanation

Let the two numbers be 3x\displaystyle 3x and 4x\displaystyle 4x. The greater number is 4x\displaystyle 4x.
According to the problem, the difference of their squares is 28\displaystyle 28:
(4x)2−(3x)2=28(4x)^2 - (3x)^2 = 28
16x2−9x2=2816x^2 - 9x^2 = 28
7x2=28  ⟹  x2=4  ⟹  x=2(since x>0)7x^2 = 28 \implies x^2 = 4 \implies x = 2 \quad (\text{since } x > 0)
The greater number is:
Greater Number=4x=4(2)=8\text{Greater Number} = 4x = 4(2) = 8

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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