If 1 is added to both the numerator and the denominator of a fraction, it becomes 4/5. If, however, 5 is subtracted from both the numerator and 1 the denominator, the fraction becomes 1/2. Find the fraction.

Let the fraction be x/y.

Given that

⇒5x + 5 = 4y + 4

⇒5x – 4y + 1 = 0 … (1)

Also given that

⇒ 2x – 10 = y – 5

⇒ 2x – y – 5 = 0 … (2)

We know that the general form for a pair of linear equations in 2 variables x and y is a₁x + b₁y + c₁ = 0

and a₂x + b₂y + c₂ = 0.

Comparing with above equations,

we have a₁ = 5, b₁ = - 4, c₁ = 1; a₂ = 2, b₂ = - 1, c₂ = - 5

We can solve by cross multiplication method using the formula

Substituting values in the formula, we get

⇒

⇒

⇒ and

⇒ x = 7 and y = 9

The fraction is 7/9.