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Mathematics

The denominator of a fraction is greater than its numerator by 9. If 7 is subtracted from both, its numerator and denominator, the fraction becomes 23\dfrac{2}{3}. Find the original fraction.

Linear Equations

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Answer

Let the numerator be x.

Given,

The denominator of a fraction is greater than its numerator by 9.

⇒ Denominator = x + 9

Thus, fraction = xx+9\dfrac{x}{x + 9}

Given,

The fraction becomes 23\dfrac{2}{3}, when 7 is subtracted from both numerator and denominator,

⇒ x−7(x+9)−7=23\dfrac{x - 7}{(x + 9) - 7} = \dfrac{2}{3}

⇒ x−7x+2=23\dfrac{x - 7}{x + 2} = \dfrac{2}{3}

⇒ 3(x - 7) = 2(x + 2)

⇒ 3x - 21 = 2x + 4

⇒ 3x - 2x = 4 + 21

⇒ x = 25.

The denominator is (x + 9) = 25 + 9 = 34.

Fraction = xy=2534\dfrac{x}{y} = \dfrac{25}{34}.

Hence, the fraction = 2534\dfrac{25}{34}.

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