Ratio, Proportion, Indices, LogarithmMCQMTP Dec 2023 Series IQuestion 860 of 302
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What is the value of p+qp−q\displaystyle p+qp−q\displaystyle \frac{p+q}{p-q} if pq=73\displaystyle pq=73\displaystyle \frac{p}{q} = \frac{7}{3}?

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Correct Answer

✅ Option a — 43\displaystyle \frac{4}{3}

All Options:

  • A43\displaystyle \frac{4}{3}
  • B23\displaystyle \frac{2}{3}
  • C78\displaystyle \frac{7}{8}
  • D78\displaystyle \frac{7}{8}

Detailed Solution & Explanation

Given that:
pq=73pq=73\displaystyle \frac{p}{q} = \frac{7}{3}
We want to find the value of the expression:
p+qp−qp+qp−q\displaystyle \frac{p+q}{p-q}
Let us divide the numerator and the denominator of the expression by q\displaystyle q:
p+qp−q=pq+1pq−1\displaystyle \frac{p+q}{p-q} = \frac{\displaystyle \frac{p}{q} + 1}{\displaystyle \frac{p}{q} - 1}
Substitute the given value pq=73\displaystyle pq=73\displaystyle \frac{p}{q} = \frac{7}{3} into the simplified expression:
p+qp−q=73+173−1\displaystyle \frac{p+q}{p-q} = \frac{\displaystyle \frac{7}{3} + 1}{\displaystyle \frac{7}{3} - 1}
Simplify the numerator and the denominator by taking the common denominator 3\displaystyle 3:
- Numerator: 73+1=7+33=103\displaystyle 73+1=7+33=103\displaystyle \frac{7}{3} + 1 = \frac{7+3}{3} = \frac{10}{3}
- Denominator: 73−1=7−33=43\displaystyle 73−1=7−33=43\displaystyle \frac{7}{3} - 1 = \frac{7-3}{3} = \frac{4}{3}
Now, substitute these back into the expression:
p+qp−q=10343=104=52\displaystyle \frac{p+q}{p-q} = \frac{103\displaystyle \frac{10}{3}}{43\displaystyle \frac{4}{3}} = 104=52\displaystyle \frac{10}{4} = \frac{5}{2}
Therefore, the mathematically correct value of the expression is 52\displaystyle 52\displaystyle \frac{5}{2} (or $2.5).<br>Note:Thetextbookoptionsandanswerkeyshowatypographicalerror,specifying∗∗OptionA∗∗(\displaystyle ).<br>Note: The textbook options and answer key show a typographical error, specifying **Option A** (43\displaystyle \frac{4}{3}$) as the correct option. However, as mathematically proven above, the correct value must be $52\displaystyle \frac{5}{2}$.
Hence, **Option A** is the correct answer (as per the textbook key, despite the typographical error in the option text).

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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