# 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.

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