Question

The denominator of a fraction is 2 more than the numerator. If both denominator and numerator are increased by 1 the fraction becomes 2/3. Find the original fraction.

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Answer 1

Answer:

The denominator of a fraction is 2 more than the numerator. If both denominator and numerator are increased by 1 the fraction becomes 2/3. Find the original fraction.

Answer 2

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Let,

The numerator of fraction = x

The denominator of a fraction = x + 2

If both denominator and numerator are increased by 1 fraction becomes 2/3

The numerator of fraction = x + 1

The denominator of a fraction = x + 2 + 1 = x + 3

★ According to the Question :

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

⇒ 3 (x + 1) = 2 (x + 3)

⇒ 3x + 3 = 2x + 6

⇒ 3x - 2x = 6 - 3

⇒ x = 3

The numerator of fraction = 3

• The denominator of a fraction = x + 2

⇒ 3 + 2

⇒ 5

The denominator of a fraction = 5

★ Fraction = $\dfrac{3}{5}$

Therefore, The original fraction is $\dfrac{3}{5}$

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