1.

The denominator of a rational number is greater than its numerator by 5. If the numerator isincreased by 11 and the denominator is decreased by 14, the new number becomes 5. Find theoriginal rational number.​

Answer»

Let the numerator of the FRACTION be x respectively.

  • The denominator of a RATIONAL NUMBER is greater than its numerator by 5.

Therefore, Denominator = (x + 5)

\qquad\quad\rule{150px}{.3ex}

A/Q,

  • According to the GIVEN condition, If the Numerator is increased by 11 and the Denominator is decreased by 14, then the number becomes 5.

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\twoheadrightarrow\:\sf Fraction = \dfrac{Numerator + 11}{Denominator - 14}

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Therefore,

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:\implies\sf \dfrac{(x + 11)}{(x + 5 - 14)} = 5 \\\\\\:\implies\sf \dfrac{(x + 11)}{(x - 9)} = 5 \\\\\\:\implies\sf (x + 11 = 5(x - 9)\\\\\\:\implies\sf x + 11 = 5x - 45\\\\\\:\implies\sf x - 5x = - 45 - 11\\\\\\:\implies\sf -4x =-56\\\\\\:\implies\sf x = \cancel\dfrac{-56}{-4}\\\\\\:\implies{\underline{\boxed{\frak{x = 14}}}}\;\bigstar

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Hence,

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  • Numerator of the fraction, x = 14
  • Denominator of the fraction, (x + 5) = (14 + 5) = 19

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\therefore{\underline{\sf{Hence,\;the\; Original\; number\;is\; \bf{\dfrac{14}{19} }.}}}


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