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 1/5. find the rational number.​

Answer 1

Answer:

$\bigstar{\bold{Fraction=\dfrac{6}{13} }}$

Step-by-step explanation:

$\Large{\underline{\bf{Given:}}}$

• Denominator of the rational number is greater than the numerator by 7
• If 3 is subtracted from the numerator and 2 is added to the denomiantor, the number becomes 1/5

$\Large{\underline{\bf{To\:Find:}}}$

• The rational number

$\Large{\underline{\bf{Solution:}}}$

⇝ Let the numerator of the fraction be x.

⇝ By given,

    Denominator = Numerator + 7

    Denominator = x + 7

⇝ Hence the fraction is,

    $\sf{The\:fraction=\dfrac{x}{x+7} }$

⇝ By given,

    Subtracting 3 from the numerator and adding 2 to the denominator, the fraction becomes 1/5.

⇝ Hence,

    $\sf{\dfrac{x-3}{x+7+2} =\dfrac{1}{5} }$

⇝ Simplifying,

    $\sf{\dfrac{x-3}{x+9} =\dfrac{1}{5} }$

⇝ Cross multiplying,

    5(x - 3) = 1 (x + 9)

    5x - 15 = x + 9

    5x - x = 9 + 15

    4x = 24

      x = 24/4

      x = 6

⇝ Hence the numerator of the fraction is 6.

⇝ Now ,

   Denominator = x + 7

   Denominator = 6 + 7 = 13

⇝ Hence the denominator of the fraction is 13.

⇝ Therefore the fraction is 6/13.

    $\boxed{\bold{Fraction=\dfrac{6}{13} }}$

$\Large{\underline{\bf{Verification:}}}$

⇝ Denominator = Numerator + 7

    13 = 6 + 7

    13 = 13

⇝ Subtracting 3 from the numerator and adding 2 to the denominator, the fraction becomes 1/5.

    $\sf{\dfrac{6-3}{13+2} =\dfrac{1}{5}}$

    3/15 = 1/5

    1/5 = 1/5

⇝ Hence verified.

Answer 2

Let the num er =x

so,x/x+7is the original rational number

Adding 2 to denominator and subtracting 3 from numerator

x-3/x+9=1/5

cross multiplying

5x-15=x+9

5x=24

x=25/4

x=6

putting x=6 in(1),we get

Required rational number=6/6+7=6/13.

please mark me as brainlist.