Ratio, Proportion, Indices, LogarithmMCQMTP Nov 19Question 850 of 305
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The third proportional to 15\displaystyle 15 and 20\displaystyle 20 is

Options

A80/3\displaystyle 80/3
B80\displaystyle 80
C80/7\displaystyle 80/7
D120\displaystyle 120
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Correct Answer

✅ Option a — 80/3\displaystyle 80/3

All Options:

  • A80/3\displaystyle 80/3
  • B80\displaystyle 80
  • C80/7\displaystyle 80/7
  • D120\displaystyle 120

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Detailed Solution & Explanation

Let a\displaystyle a and b\displaystyle b be two numbers. If x\displaystyle x is the third proportional to a\displaystyle a and b\displaystyle b, it means that a\displaystyle a, b\displaystyle b, and x\displaystyle x are in continued proportion. This relationship is expressed as: a:b::b:xa : b :: b : x This implies that the ratio of the first term to the second term is equal to the ratio of the second term to the third term.
Mathematically, this can be written as: ab=bx\frac{a}{b} = \frac{b}{x}
In this question, the two given numbers are 15\displaystyle 15 and 20\displaystyle 20. So, we have a=15\displaystyle a = 15 and b=20\displaystyle b = 20. We need to find the third proportional, which we denote as x\displaystyle x.
Substitute the values of a\displaystyle a and b\displaystyle b into the formula: 1520=20x\frac{15}{20} = \frac{20}{x}
To solve for x\displaystyle x, we can cross-multiply the terms: 15×x=20×2015 \times x = 20 \times 20 15x=40015x = 400
Now, divide both sides of the equation by 15\displaystyle 15 to find the value of x\displaystyle x: x=40015x = \frac{400}{15}
To simplify the fraction, we can divide both the numerator and the denominator by their greatest common divisor, which is 5\displaystyle 5: x=400÷515÷5x = \frac{400 \div 5}{15 \div 5} x=803x = \frac{80}{3}
Comparing this result with the given options: (A) 80/3\displaystyle 80/3 (B) 80\displaystyle 80 (C) 80/7\displaystyle 80/7 (D) 120\displaystyle 120
Our calculated value x=803\displaystyle x = \frac{80}{3} matches **Option A**. Therefore, the correct choice is **Option A**.

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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