If 2 is added to the numerator of a fraction, it reduces to 1/2 and if 1 is subtracted from the denominator, it reduces to 1/3. Find the fraction.

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Solution

Let the numerator and denominator of the fraction be x and y respectively. Then the fraction is

If 2 is added to the numerator of the fraction, it reduces to. Thus, we have

If 1 is subtracted from the denominator, the fraction reduces to. Thus, we have

So, we have two equations

Here x and y are unknowns. We have to solve the above equations for x and y.

By using cross-multiplication, we have

Hence, the fraction is.

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