If p:q is the sub-duplicate ratio of p-x2:q-x2 , then x2 is

Option d: None of these. Solution: Let the given ratio be p : q , which is the sub-duplicate ratio of (p - x2) : (q - x2) . By the definition of the sub-duplicate ratio, we have: p/q = sqrt(p - x2/q - x2) Squaring both sides of the equation: p2/q2 = p - x2/q - x2 Cross-multiplying to solve for x2 : p2(q - x2) = q2(p - x2) p2q - p2x2 = q2p - q2x2 Rearranging terms to group all x2 terms on one side: q2x2 - p2x2 = q2p - p2q Factoring out x2 and pq respectively: x2(q2 - p2) = pq(q - p) Applying the difference of squares identity q2 - p2 = (q - p)(q + p) : x2(q - p)(q + p) = pq(q - p) Assuming p ≠ q , we divide both sides by (q - p) : x2(p + q) = pq x2 = pq/p + q Comparing with the given choices: - Option A: p/p+q - Option B: q/p+q - Option C: qp/p-q None of these represents the correct expression pq/p+q . Hence, the correct choice is None of these.

If $p:q$ is the sub-duplicate ratio of $p-x^2:q-x^2$, then $x^2$ is

The correct answer is Option d: None of these. Let the given ratio be $p : q$, which is the sub-duplicate ratio of $(p - x^2) : (q - x^2)$. By the definition of the sub-duplicate ratio, we have: $$\frac{p}{q} = \sqrt{\frac{p - x^2}{q - x^2}}$$ Squaring both sides of the equation: $$\frac{p^2}{q^2} = \frac{p - x^2}{q - x^2}$$ Cross-multiplying to solve for $x^2$: $$p^2(q - x^2) = q^2(p - x^2)$$ $$p^2q - p^2x^2 = q^2p - q^2x^2$$ Rearranging terms to group all $x^2$ terms on one side: $$q^2x^2 - p^2x^2 = q^2p - p^2q$$ Factoring out $x^2$ and $pq$ respectively: $$x^2(q^2 - p^2) = pq(q - p)$$ Applying the difference of squares identity $q^2 - p^2 = (q - p)(q + p)$: $$x^2(q - p)(q + p) = pq(q - p)$$ Assuming $p \neq q$, we divide both sides by $(q - p)$: $$x^2(p + q) = pq \implies x^2 = \frac{pq}{p + q}$$ Comparing with the given choices: - Option A: $\frac{p}{p+q}$ - Option B: $\frac{q}{p+q}$ - Option C: $\frac{qp}{p-q}$ None of these represents the correct expression $\frac{pq}{p+q}$. Hence, the correct choice is **None of these**.

Ratio, Proportion, Indices, LogarithmMCQPYQ May 18Question 787 of 305

All Questions

If $\displaystyle p:q$ is the sub-duplicate ratio of $\displaystyle p-x^2:q-x^2$ , then $\displaystyle x^2$ is

Options

\displaystyle \frac{p}{p+q}

\displaystyle \frac{q}{p+q}

\displaystyle qp

DNone of these

For any discrepancies in this question, email contact@cadada.in

Correct Answer

✅ Option d — None of these

All Options:

A $\displaystyle \frac{p}{p+q}$
B $\displaystyle \frac{q}{p+q}$
C $\displaystyle qp$
DNone of these

Detailed Solution & Explanation

Let the given ratio be

\displaystyle p : q

, which is the sub-duplicate ratio of

\displaystyle (p - x^2) : (q - x^2)

.
By the definition of the sub-duplicate ratio, we have:

\frac{p}{q} = \sqrt{\frac{p - x^2}{q - x^2}}

Squaring both sides of the equation:

\frac{p^2}{q^2} = \frac{p - x^2}{q - x^2}

Cross-multiplying to solve for

\displaystyle x^2

p^2(q - x^2) = q^2(p - x^2)

p^2q - p^2x^2 = q^2p - q^2x^2

Rearranging terms to group all

\displaystyle x^2

terms on one side:

q^2x^2 - p^2x^2 = q^2p - p^2q

Factoring out

\displaystyle x^2

and

\displaystyle pq

respectively:

x^2(q^2 - p^2) = pq(q - p)

Applying the difference of squares identity

\displaystyle q^2 - p^2 = (q - p)(q + p)

x^2(q - p)(q + p) = pq(q - p)

Assuming

\displaystyle p \neq q

, we divide both sides by

\displaystyle (q - p)

x^2(p + q) = pq \implies x^2 = \frac{pq}{p + q}

Comparing with the given choices:
- Option A:

\displaystyle \frac{p}{p+q}

- Option B:

\displaystyle \frac{q}{p+q}

- Option C:

\displaystyle \frac{qp}{p-q}

None of these represents the correct expression

\displaystyle \frac{pq}{p+q}

. Hence, the correct choice is **None of these**.

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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If p:q\displaystyle p:qp:q is the sub-duplicate ratio of p−x2:q−x2\displaystyle p-x^2:q-x^2p−x2:q−x2, then x2\displaystyle x^2x2 is