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

Solution :-

Let :-

Numerator = x

Denominator = y

According to the first condition :-

$\longrightarrow \sf y = x+7 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ ..................(1)$

According to the second condition :-

$\longrightarrow \sf \dfrac{x-3}{y+2} = \dfrac{1}{5} \\\\\longrightarrow 5(x-3) = y+2 \\\\\longrightarrow 5x-15 = y +2 \\\\\longrightarrow 5x-y = 17 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ ..................(2)$

Substitute the value of y in eq (2) :-

$\longrightarrow \sf 5x-(x+7)= 17 \\\\\longrightarrow 5x-x-7 = 17 \\\\\longrightarrow 5x-x = 17+7\\\\\longrightarrow 4x = 24 \\\\\longrightarrow \bf x = 6$

Substitute x = 6 in eq (1) :-

$\longrightarrow \sf y = 6+7 \\\\\longrightarrow \bf y = 13$

$\bf FRACTION = \dfrac{6}{13}$

Answer 2

Step-by-step explanation:

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

To Find :

• The rational number

Solution :

Let the numerator of the fraction be x.

    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,

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

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

Cross multiplying,

    5(x - 3) = 1 (x + 9)

    5x - 15 = x + 9

    5x - x = 9 + 15

    4x = 24

      x = 24/4

      x = 6

   Denominator = x + 7

   Denominator = 6 + 7 = 13

Therefore the fraction is 6/13.