Ratio, Proportion, Indices, LogarithmMCQMTP Nov 19Question 850 of 302
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The third proportional to $15\displaystyle and $20 is

Select Your Answer (Keyboard: A, B, C, D)
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Correct Answer

✅ Option a — $80/3$

All Options:

  • A$80/3$
  • B$80$
  • C$80/7$
  • D$120$

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=bxab=bx\displaystyle \frac{a}{b} = \frac{b}{x}
In this question, the two given numbers are $15\displaystyle and $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=20x1520=20x\displaystyle \frac{15}{20} = \frac{20}{x}
To solve for x\displaystyle x, we can cross-multiply the terms: 15×x=20×2015 ×\displaystyle \times x = 20 ×\displaystyle \times 20 15x=40015x = 400
Now, divide both sides of the equation by $15$ to find the value of $x$: x=40015x = 40015\displaystyle \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 = 400÷515÷5\displaystyle \frac{400 \div 5}{15 \div 5} x=803x = 803\displaystyle \frac{80}{3}
Comparing this result with the given options: (A) $80/3$ (B) $80$ (C) $80/7$ (D) $120$
Our calculated value x=803\displaystyle x = 803\displaystyle \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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