Question

The numerator of a fraction is 3 less than the denominator. If 2 is added to both the numerator and the denominator, then the sum of the new fraction and the original fraction is 29/20. Find the original fraction

Answer 1

Answer:

Step-by-step explanation:

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Answer 2

Answer:

Step-by-step explanation:

Solution :-

Let the denominator of fraction be x.

Then, its numerator be (x - 3),

Fraction = x - 3/x

According to the Question,

⇒ (x - 3) + 2/x + 2 + (x - 3)/x = 29/20

⇒ (x - 1)/(x + 2) + (x - 3)/x = 29/20

⇒ x(x - 1) + (x - 3) (x + 2)/x(x + 2) = 29/20

⇒ (x² - x) + (x² - x - 6)/x² + 2x = 29/20

⇒ 20(2x² - 2x - 6) = 29(x² + 2x)

⇒ 40x² - 40x - 120 = 29x² + 58x

⇒ 11x² - 98x - 120 = 0

⇒ 11x² - 110x + 12x - 120 = 0

⇒ 11x(x - 10) + 12(x - 10) = 0

⇒ (x - 10) (11x + 12) = 0

⇒ x - 10 = 0 or 11x + 12 = 0

⇒ x = 10, - 12/11 (As x can't be negative)

⇒ x = 10

Denominator = x = 10

Numerator = x - 3 = 10 - 3 = 7

Fraction = 7/10

Hence, the required fraction is 7/10.