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.