Question

Q.3) 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. Find the original rational number​

Answer 1

Answer:

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 :-

• What is the original rational number.

Solution :-

Let,

$\mapsto \sf\bold{Numerator = x}$

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

Hence, the required original rational number is :

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

$\leadsto \sf\bold{\green{\dfrac{x}{x + 3}}}$

According to the question,

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

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

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

By doing cross multiplication we get,

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

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

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

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

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

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

$\implies \sf \bold{\purple{x =\: 5}}$

Hence, the required original rational number is ;

$\longrightarrow \sf \dfrac{x}{x + 3}$

$\longrightarrow \sf \dfrac{5}{5 + 3}$

$\longrightarrow \sf\bold{\red{\dfrac{5}{8}}}$

${\normalsize{\bold{\underline{\therefore\: The\: original\: rational\: number\: is\: \dfrac{5}{8}\: .}}}}$

Answer 2

Solution -

• The denominator of a rational number is greater than the numerator by 3.

• If 3 is subtracted from the numerator and 2 is added to the denominator , the new number becomes ⅕ .

We have to find the original rational number .

For this, let's start by assigning the numerator of the rational number a value of x.

The denominator of a rational number is greater than the numerator by 3, as mentioned above.

Therefore the denominator becomes (x+3).

The rational number becomes x/x+3 .

3 is subtracted from the numerator and 2 is added to the denominator.

New number >

> ( x - 3)/( x + 5)

This is equal to ⅕ .

( x - 3)/( x + 5) = ⅕

> 5x - 15 = x + 5

> 4x = 20

> x = 5.

Thus , the original rational number is 5/8. This is the required answer .

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