Question

8.
The denominator of a rational number is greater than its numerator by 7. if 3 is subtracted from the numerator and 2 is added to its denominator, the new
number becomes Find the rational number.
1
5​

Answer 1

Answer:

6/13

Step-by-step explanation:

Let the numerator be x and the denominator be x+7

BTP

x-3/x+7+2= 1/5

= x-3/x+9= 1/5

=5x-15 = x+9 ( Cross Multiplication)

= 4x= 24

= x= 6 ( Numerator )

x+7 = 13 ( Denominator )

Answer 2

Appropriate Question:

• The denominator of a rational number is greater than its numerator by 7. If 3 is subtracted from the numerator and 2 is added to its denominator, the new number becomes ⅕. Find the rational number.

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$\sf Given \begin{cases} & \sf{Denominator = \bf{x + 7}} \\ \\ & \sf{\dfrac{Numerator - 3}{Denominator + 2} = \bf{ \dfrac{1}{5}}} \end{cases}$

Need To find: The rational number.

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☯ Let Numerator and Denominator of a rational number be x and (x + 7).⠀⠀⠀

Given that,

• The denominator of a rational number is greater than its numerator by 7. And, when two is added to the denominator.

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Therefore,

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$:\implies\sf Fraction = \dfrac{x - 3}{x + 9}$

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$\underline{\bigstar\:\boldsymbol{According\:to\:the\:question\::}}$

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$:\implies\sf \dfrac{(x -3)}{(x + 9)} = \dfrac{1}{5} \\\\\\:\implies\sf x + 9 = 5(x - 3) \\\\\\:\implies\sf x + 9 = 5x - 15\\\\\\:\implies\sf 9 + 15 = 5x - x\\\\\\:\implies\sf 24 = 4x\\\\\\:\implies\sf x = \cancel\dfrac{24}{4}\\\\\\:\implies{\underline{\boxed{\frak{\pink{x = 6}}}}}\;\bigstar$

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Hence,

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• Numerator of the fraction, x = 6

• Denominator of the fraction, (x + 7) = (6 + 7) = 13.

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$\therefore{\underline{\sf{Hence,\; the \; required\; number\: is \; \textbf{ {}^{\text6}\!/{}_{\text{13}} }}}}.$