Question

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

Answer 1

Step-by-step explanation:

Let the required number be

y

x

.

Since denominator of the number is greater than its numerator by 3.

∴y=x+3.....(1)

Also,

y+2

x−3

=

5

1

5(x−3)=y+2

5x−15=(x+3)+2

5x−15=x+5

5x−x=15+5

⇒x=

4

20

=5

Substituting the value of x in equation (1), we have

y=5+3=8

Therefore,

Required no. =

8

5

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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$\underline{\underline{\bf{\dfrac{5}{8}}}}.$

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