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Question

If 2 is added to the numerator of a fraction, it reduces to 12 and if 1is subtracted from the denominator, it reduces to13.

Find the fraction.


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Solution

Step 1: Framing the equations.

Assume x is the numerator andyis the denominator.

Given: 2 is added to the numerator of a fraction, it reduces to 12.

Thus, x+2y=12

2(x+2)=y2x+4=y

2x-y=-4……………1

Also given that 1 is subtracted from the denominator of a fraction, it reduces to 13.

Thus, xy-1=13

3x=y-1

3x-y=-1…………… 2

Step 2 : Solving the simultaneous equations.

Subtract equation 2 from equation 1.

2x-y-3x+y=-4+1-x=-3x=3

Now, put the value of x in equation 2.

2(3)-y=-46-y=-4-y=-10y=10

Hence, the fraction is 310.


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