Ratio, Proportion, Indices, LogarithmMCQMTP Apr 21Question 828 of 302
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If pq=23\displaystyle pq=23\displaystyle \frac{p}{q} = \frac{2}{3}, then the value of 2p−q2p+q\displaystyle 2p−q2p+q\displaystyle \frac{2p-q}{2p+q} is:

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

✅ Option c — 1/7\displaystyle 1/7

All Options:

  • A1\displaystyle 1
  • B−1/7\displaystyle -1/7
  • C1/7\displaystyle 1/7
  • D7\displaystyle 7

Detailed Solution & Explanation

We are given the ratio: pq=23pq=23\displaystyle \frac{p}{q} = \frac{2}{3} We need to find the value of the expression 2p−q2p+q\displaystyle 2p−q2p+q\displaystyle \frac{2p-q}{2p+q}. To simplify the expression, we can divide both the numerator and the denominator by q\displaystyle q. This is a valid operation as long as q≠0\displaystyle q ≠\displaystyle \neq 0. If q=0\displaystyle q=0, then pq\displaystyle pq\displaystyle \frac{p}{q} would be undefined, which contradicts the given information. 2p−q2p+q=2p−qq2p+qq\displaystyle \frac{2p-q}{2p+q} = \frac{2p−qq\displaystyle \frac{2p-q}{q}}{2p+qq\displaystyle \frac{2p+q}{q}} Now, we distribute the division by q\displaystyle q in both the numerator and the denominator: =2pq−qq2pq+qq= 2pq−qq2pq+qq\displaystyle \frac{\frac{2p}{q} - \frac{q}{q}}{\frac{2p}{q} + \frac{q}{q}} Simplify the terms: =2(pq)−12(pq)+1= 2(pq)−12(pq)+1\displaystyle \frac{2\left(\frac{p}{q}\right) - 1}{2\left(\frac{p}{q}\right) + 1} We are given that pq=23\displaystyle pq=23\displaystyle \frac{p}{q} = \frac{2}{3}. Substitute this value into the expression: =2(23)−12(23)+1= 2(23)−12(23)+1\displaystyle \frac{2\left(\frac{2}{3}\right) - 1}{2\left(\frac{2}{3}\right) + 1} Perform the multiplication in the numerator and denominator: =43−143+1= 43−143+1\displaystyle \frac{\frac{4}{3} - 1}{\frac{4}{3} + 1} To perform the subtraction and addition, we express 1\displaystyle 1 as 33\displaystyle 33\displaystyle \frac{3}{3}: =43−3343+33= 43−3343+33\displaystyle \frac{\frac{4}{3} - \frac{3}{3}}{\frac{4}{3} + \frac{3}{3}} Now, perform the subtraction in the numerator and the addition in the denominator: =4−334+33= 4−334+33\displaystyle \frac{\frac{4-3}{3}}{\frac{4+3}{3}} $$ = \frac{\frac{1

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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