Ratio, Proportion, Indices, LogarithmMCQMTP Apr 21Question 852 of 305
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The third proportional to 9\displaystyle 9 and 25\displaystyle 25

Options

A80/3\displaystyle 80/3
B80\displaystyle 80
C80/7\displaystyle 80/7
DNone of these
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Correct Answer

✅ Option d — None of these

All Options:

  • A80/3\displaystyle 80/3
  • B80\displaystyle 80
  • C80/7\displaystyle 80/7
  • DNone of these

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Detailed Solution & Explanation

The concept of a third proportional is derived from continued proportion. If three numbers, say a\displaystyle a, b\displaystyle b, and c\displaystyle c, are in continued proportion, it means that the ratio of the first number to the second number is equal to the ratio of the second number to the third number. This relationship is expressed as a:b::b:c\displaystyle a:b::b:c. In fractional form, this proportion is written as: ab=bc\frac{a}{b} = \frac{b}{c} Here, c\displaystyle c is defined as the third proportional to a\displaystyle a and b\displaystyle b. Given in the question are the first two numbers: The first number, a=9\displaystyle a = 9. The second number, b=25\displaystyle b = 25. We need to find the third proportional, which we will denote as c\displaystyle c. Substitute the given values of a\displaystyle a and b\displaystyle b into the formula for continued proportion: 925=25c\frac{9}{25} = \frac{25}{c} To solve for c\displaystyle c, we can use the property of proportions that the product of the means equals the product of the extremes (cross-multiplication): 9×c=25×25\displaystyle 9 \times c = 25 \times 25 Perform the multiplication on the right side: 9c=625\displaystyle 9c = 625 Now, to find c\displaystyle c, divide both sides of the equation by 9\displaystyle 9: c=6259c = \frac{625}{9} This is the exact value of the third proportional to 9\displaystyle 9 and 25\displaystyle 25. Next, we compare this calculated value with the given options: (A) 80/3\displaystyle 80/3 (B) 80\displaystyle 80 (C) 80/7\displaystyle 80/7 (D) None of

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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