Allied & ICAR Exam Bank • ALLIED_2431 MCQ • 2 Marks

Section 8: General Aptitude

Quantitative Aptitude

Subtopic: Ratios & Percentages

Question Statement:

If $a:b$ is the sub-duplicate ratio of $(a - x):(b - x)$, then $x$ is equal to:

Options:

  • (A) $\frac{ab}{a + b}$
  • (B) $\frac{a + b}{ab}$
  • (C) $ab$
  • (D) $\frac{a - b}{a + b}$

Answer Key:

A

Step-by-Step Solution & Explanation

$(a-x)/(b-x) = a^2/b^2 \implies b^2(a-x) = a^2(b-x) \implies ab^2 - b^2x = a^2b - a^2x \implies x(a^2 - b^2) = ab(a - b) \implies x(a+b)(a-b) = ab(a-b) \implies x = \frac{ab}{a+b}$.
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