Question

The denominator of a rational number is greater than its numerator by 4. If numerator is increased by 11 and
the denominator is decreased by 1, the new number becomes 7/3 Find the original number.
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Answer 1

Given :-

The denominator of a rational number is greater than its numerator by 4. If numerator is increased by 11 and  the denominator is decreased by 1, the new number becomes 7/3

To Find :-

Original number

Solution :-

Let the numerator be x. Then, denominator will be x + 4

x + 11/x + 4 - 1 = 7/3

x + 11/x + 3 = 7/3

3(x + 11) = 7(x + 3)

3x + 33 = 7x + 21

3x - 7x = 21 - 33

-4x = -12

x = -12/-4

x = 12/4

x = 3

Therefore

Numerator = x = 3

Denominator = x + 4 = 3 + 4 = 7

Fraction = 3/7

Answer 2

Given: The denominator of a rational number is greater than it's numerator by 4. If the numerator is increased by 11 and the Denominator is decreased by 1, the new number becomes ⁷⁄₃.

Need to find: The Original number?

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❍ Let's say, that the numerator of the fraction be x. Then, denominator of the fraction be (x + 4) respectively.

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$\underline{\bigstar\:\boldsymbol{According \;to\;the\; Question\; :}}$⠀⠀

• If the numerator is increased by 11 and the Denominator is decreased by 1, the new number becomes ⁷⁄₃.

⠀⠀⠀

$\twoheadrightarrow\sf\Bigg\{\dfrac{x + 11}{x + 4 - 1}\Bigg\} = \Bigg\{\dfrac{7}{3}\Bigg\}\\\\\\\twoheadrightarrow\sf\Bigg\{\dfrac{x + 11}{x + 3}\Bigg\} = \Bigg\{\dfrac{7}{3}\Bigg\}\\\\\\\twoheadrightarrow\sf 3\Big\{x + 11\Big\}=7\Big\{x + 3\Big\}\\\\\\\twoheadrightarrow\sf 3x + 33 = 7x + 21 \\\\\\\twoheadrightarrow\sf 3x - 7x = 21 - 33\\\\\\\twoheadrightarrow\sf -4x = -12\\\\\\\twoheadrightarrow\sf x = \cancel\dfrac{-12}{-4}\\\\\\\twoheadrightarrow\underline{\boxed{\pmb{\frak{x = 3}}}}\;\bigstar$

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Therefore,

• Numerator of the fraction, x = 3
• Denominator of the fraction, (x + 4) = (3 + 4) = 7

⠀

$\therefore{\underline{\sf{Hence,\: the \;original\; number\; is\; \bf{\dfrac{3}{7}}}.}}$