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Question

When 3 is added to the denominator and 2 is subtracted from the numerator a fraction becomes 1/4. And when 6 is added to numerator and the denominator is multiplied by 3, it becomes 2/3. 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 3 is added to the denominator and 2 is subtracted from the numerator, the fraction becomes. Thus, we have

If 6 is added to the numerator and the denominator is multiplied by 3, the fraction becomes. 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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