Question

The denominator of a rational number is less than its numerator than 5. If 5 is added to the numerator,
the new number becomes
Find the original rational number
11/6. Find the original numars​

Answer 1

☯ The denominator of a rational number is less than its numerator than 5. So,

Let the numerator of rational number be x.

Therefore, denominator of rational number is (x - 5).

$:\implies\sf Fraction = \dfrac{x}{x - 5}$

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$\qquad\qquad\boxed{\bf{\mid{\overline{\underline{\purple{\bigstar\: According\: to \: Question :}}}}}\mid}$

☯ If 5 is added to the numerator, the new number becomes 11/6.

$:\implies\sf \dfrac{x + 5}{x - 5} = \dfrac{11}{6}$

$:\implies\sf 6(x + 5) = 11(x - 5)$

$:\implies\sf 6x + 30 = 11x - 55$

$:\implies\sf 6x - 11x = - 55 - 30$

$:\implies\sf - 5x = - 85$

$:\implies\sf x = \cancel{ \dfrac{- 85}{- 5}}$

$:\implies{\boxed{\frak{\pink{x = 17}}}}\;\bigstar$

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Therefore,

• Numerator, x = 17

• Denominator, (x - 5) = 17 - 5 = 12

$\therefore$ Hence, The required rational number is 17/12.