Q. 195.0( 6 Votes )

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.

Answer :

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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