Question

the numerator of a fraction is 8 less than its denominator. if 12 is added to both numerator and denominator, the fraction becomes 11/19.find the fraction

Answer 1

Given:-

⠀⠀⠀◍ The numerator of a fraction is 8 ⠀⠀⠀⠀less than its denominator.

⠀⠀⠀◍ If 12 is added to both numerator ⠀⠀⠀⠀and denominator, the fraction ⠀⠀⠀⠀becomes 11/19.

⠀

To find:-

⠀⠀⠀◍ The fraction.

⠀

Let:-

⠀⠀⠀◍ Fraction be

⠀⠀⠀◍ $\sf\dfrac{x}{y}$

⠀

According to the question

⠀⠀⠀✯ x = y - 8⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀Eq......... i

⠀⠀⠀✯ $\sf\dfrac{x + 12}{y + 12}$ = $\dfrac{11}{19}$

⠀

⠀

Solution:-

⠀⠀⠀✯ 19 (x + 12) = 11 (y + 12)

⠀⠀⠀✯ 19x + 228 = 11 y + 132

⠀⠀⠀✯ 19x - 11y = 132 - 228

⠀⠀⠀✯ 19x - 11y = -96

⠀⠀⠀✯ 19 (y - 8) - 11y = -96

⠀⠀⠀✯ 19y - 152 - 11y = -96

⠀⠀⠀✯ 8y = -96 + 152

⠀⠀⠀✯ y = $\sf\dfrac{56}{8}$

⠀⠀⠀✯ y = 7

⠀

◍ Putting the value of y in Eq...... i

⠀⠀⠀✯ x = y - 8

⠀⠀⠀✯ x = 7 - 8

⠀⠀⠀✯ x = -1

⠀

⠀

Answer:-

⠀⠀⠀★ The fraction = $\sf\dfrac{x}{y}$

⠀⠀⠀★ The fraction = $\sf\dfrac{-1}{7}$

Answer 2

Given:-

• The numerator of a fraction is 8 less than its denominator.
• 12 is added to both numerator and denominator, the fraction becomes 11/19.

⠀

To Find:-

• Find the required fraction.

Solution :)

So, let's consider the unknown fraction be "x/y"⠀

Now,

From the given

The numerator of a fraction is 8 less than its denominator.

⠀⠀

⇒ x = y - 8⠀........(1)

Now,

{x + 12}/{y + 12} = $\dfrac{11}{19}$

By cross multiplication method

⇒ 19 (x + 12) = 11 (y + 12)

⇒ 19x + 228 = 11 y + 132

⇒ 19x - 11y = 132 - 228

⇒ 19x - 11y = -96

⇒ 19 (y - 8) - 11y = -96

⇒ 19y - 152 - 11y = -96

⇒ 8y = -96 + 152

⇒ y = 56 / 8

⇒ y = 7

⠀

Substituting the value of y in Equation ..(1)

⇒ x = y - 8

⇒ x = 7 - 8

⇒ x = -1

Therefore,

• The required fraction = $\sf\dfrac{x}{y}$
• Fraction is -1/7

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