If 1 is added to both the numerator and the denominator of a fraction, it becomes \(\dfrac{2}{3}\). If 2 is subtracted from both the numerator and the denominator, it becomes \(\dfrac{1}{2}\). Find the fraction.

Doubtly Asked 29 Oct 2026 Practice test ssc 10th Save WhatsApp Report

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Answer: The fraction is \(\dfrac{5}{8}\)

Let the fraction be \(\dfrac{x}{y}\).

Condition 1: \(\dfrac{x + 1}{y + 1} = \dfrac{2}{3} \Rightarrow 3x + 3 = 2y + 2 \Rightarrow 3x - 2y = -1\) …(I)

Condition 2: \(\dfrac{x - 2}{y - 2} = \dfrac{1}{2} \Rightarrow 2x - 4 = y - 2 \Rightarrow 2x - y = 2\) …(II)

Multiply (II) by 2: \(4x - 2y = 4\) …(III)

(III) − (I): \(x = 5\). From (II): \(y = 2(5) - 2 = 8\).

Check: \(\dfrac{6}{9} = \dfrac{2}{3}\) ✓, \(\dfrac{3}{6} = \dfrac{1}{2}\) ✓. The fraction is \(\dfrac{5}{8}\).

Doubtly AI · 29 Oct 2026 AI-verified · Nov 2026 Report

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