Question

the denominator of a rational number is greater than its numerator by 3 If 3 is subtracted from the numerator and two is added to the denominator the number becomes 1/5
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Answer 1

Answer:

Question to be asked :-

The Denominator of a fraction is greater than its numerator by 3. If 3 is subtracted from the numerator and 2 is added to the denominator then the fraction become ⅕. Find orginal Fraction.

Given :-

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

To Find :-

Fraction

Solution :-

Let us assume the fraction be :-

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

Now,

When 3 is subtracted from numerator and 2 added to denominator

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

$\dag \mathfrak \red{cross \: multiplication}$

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

$\tt \: x + 5 = 5x - 15$

$\tt \: 15 + 5 = 5x - x$

$\tt \: 20 = 4x$

$\tt \: x = \cancel \dfrac{20}{4}$

$\tt \: x = 5$

$\tt \: \dfrac{x}{x + 3} = \dfrac{5}{5 + 3} = \dfrac{5}{8}$

Answer 2

Answer:

Given :-

• The denominator of a rational number is greater than its numerator by 3. If 3 is substracted from the numerator and two is added to the denominator the number becomes ⅕.

To Find :-

• What is the original fraction.

Solution :-

Let, the numerator be x

And, the denominator will be x + 3

Then, the fraction is $\sf\dfrac{x}{x + 3}$

According to the question,

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

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

By doing cross multiplication we get,

⇒ 5(x - 3) = x + 5

⇒ 5x - 15 = x + 5

⇒ 5x - x = 5 + 15

⇒ 4x = 20

⇒ x = $\sf\dfrac{\cancel{20}}{\cancel{4}}$

➠ x = 5

Hence, the required original fraction are,

↦ $\sf\dfrac{x}{x + 3}$

↦ $\sf\dfrac{5}{5 + 3}$

➦ $\sf\dfrac{5}{8}$

$\therefore$ The original fraction is $\boxed{\bold{\large{\dfrac{5}{8}}}}$ .

Let's Verify :-

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

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

Put x = 5 we get,

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

↪ $\sf\dfrac{2}{10} =\: \dfrac{1}{5}$

↪ $\sf\dfrac{\cancel{2}}{\cancel{10}} =\: \dfrac{1}{5}$

↪ $\sf\dfrac{1}{5} =\: \dfrac{1}{5}$

➥ LHS= RHS

Hence, Verified ✔