1.

A fraction becomes equal to 4/5 if 1 is added both numerator and denominator. If however 5 is substracted from both numerator and denominator the fraction becomes equal to 1/2. What is the fraction.

Answer»

Answer:

Step-by-step explanation:

GIVEN,

  • A FRACTION BECOMES equal to 4/5 if 1 is added both numerator and denominator.
  • If however 5 is substracted from both numerator and denominator the fraction becomes equal to 1/2.

To Find,

  • The Fraction.

Solution,

Let the fraction be x/y.

Then,

According to the QUESTION,

x + 1/y + 1 = 4/5

And, x - 5/y - 5 = 1/2

⇒ 5x + 5 = 4y and 2x - 10 = y - 5

⇒ 5x - 4y + 1 = 0 and 2x - y - 5 = 0

By using cross-multiplication, we have

⇒ x/- 4 × (- 5) - (- 1) × 1 = - y/5 × (- 5) - 2 × 1 = 1/5 × (- 1) - 2 × (- 4)

⇒ x/20 + 1 = y/25 + 2 = 1/- 5 + 8

⇒ x/21 = y/27 = 1/3

⇒ x = 21/3 = 7

⇒ y = 27/3 = 9

Hence, the required fraction is 7/9.


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