If 1 is added to the numerator of a fraction, it becomes 1/5 ; if 1 is taken from the denominator, it becomes 1/7 , find the fraction.

Let numerator be x and denominator be y. Given, if 1 is added to the numerator of a fraction, it becomes . y = 5(x + 1) .......(i) Given, if 1 is taken from the denominator, it becomes . ⇒ y - 1 = 7x ⇒ y = 1 + 7x ........(ii) Equating (i) and (ii) we get, ⇒ 5(x + 1) = 1 + 7x ⇒ 5x + 5 = 1 + 7x ⇒ 7x - 5x = 5 - 1 ⇒ 2x = 4 ⇒ x = 2. Substituting value of x in (ii) we get, y = 1 + 7x = 1 + 7(2) = 1 + 14 = 15. Original fraction = . Hence, fraction = .

Mathematics

If 1 is added to the numerator of a fraction, it becomes $\dfrac{1}{5}$ ; if 1 is taken from the denominator, it becomes $\dfrac{1}{7}$ , find the fraction.

Linear Equations

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Answer

Let numerator be x and denominator be y.

Given, if 1 is added to the numerator of a fraction, it becomes $\dfrac{1}{5}$ .

$\therefore \dfrac{x + 1}{y} = \dfrac{1}{5}$

y = 5(x + 1) …….(i)

Given, if 1 is taken from the denominator, it becomes $\dfrac{1}{7}$ .

$\therefore \dfrac{x}{y - 1} = \dfrac{1}{7}$

⇒ y - 1 = 7x
⇒ y = 1 + 7x ……..(ii)

Equating (i) and (ii) we get,

⇒ 5(x + 1) = 1 + 7x

⇒ 5x + 5 = 1 + 7x

⇒ 7x - 5x = 5 - 1

⇒ 2x = 4

⇒ x = 2.

Substituting value of x in (ii) we get,

y = 1 + 7x = 1 + 7(2) = 1 + 14 = 15.

Original fraction = $\dfrac{x}{y} = \dfrac{2}{15}$ .

Hence, fraction = $\dfrac{2}{15}$ .

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Mathematics

If 1 is added to the numerator of a fraction, it becomes $\dfrac{1}{5}$ ; if 1 is taken from the denominator, it becomes $\dfrac{1}{7}$ , find the fraction.

Linear Equations

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