Question

The denominator of a rational number is greater than its numerator by 3 if 3 is subtracted from the numerator and 2 is added to it's denominator the new number become 1/5 find the original number

Answer 1

Hiii friend,

Let the numerator of a fraction be X.

Denominator = (X+3)


Fraction = Numerator/Denominator = (X)/(X+3)

3 is subtracted from the numerator then the numerator becomes (X-3) and 2 is added to it's denominator then the Denominator becomes (X+3+2) .


Fraction = Numerator/Denominator = (X-3)/(X+3+2).


According to question,

(X-3)/(X+3+2) = 1/5

X-3/X+5 = 1/5

5(X-3) = 1(X+5)

5X - 15 = X + 5

5X - X = 5+15

4X = 20


X = 20/4 => 5


Numerator = X = 5

And,

Denominator = (X+3) => (5+3) = 8


Fraction = Numerator/Denominator = 5/8


HOPE IT WILL HELP YOU...... :-)

Answer 2

Given:-

• The denominator of a rational number is greater than its numerator by 3. If 3 is subtracted from its numerator and 2 is added to its denominator, the new number becomes 1/5.

To Find:-

• Original rational number.

Solution:-

Let,

$\mapsto \sf{Numerator = x}$

$\mapsto \sf{Denominator =\: x + 3}$

Hence, the required original rational number is :

$\mapsto \sf \dfrac{Numerator}{Denominator}$

$\mapsto{\boxed{\sf{\dfrac{x}{x + 3}}}}\red\bigstar$

According to the question,

$\begin{gathered}:\implies \sf \dfrac{Numerator - 3}{Denominator + 2} =\: New \: Number\\\end{gathered}$

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

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

By doing cross multiplication we get,

$:\implies \sf 5(x - 3) =\: 1(x + 5)$

$:\implies \sf 5x - 15 =\: x + 5)$

$:\implies \sf 5x - x =\: 5 + 15$

$:\implies \sf 4x =\: 20$

$:\implies \sf x =\: \dfrac{\cancel{20}}{\cancel{4}}$

$:\implies \sf x =\: \dfrac{5}{1}$

$: \implies   \underline{\boxed{ \frak{x=5}}} \blue \bigstar$

Hence, the required original rational number is;

$:\implies\sf \dfrac{x}{x + 3}$

$:\implies \sf \dfrac{5}{5 + 3}$

$:\implies\underline{\boxed{\frak{\dfrac{5}{8}}}}\pink\bigstar$

• The original rational number is$\underline{\underline{\bf{\dfrac{5}{8}}}}.$

Thank you!!

@itzshivani