Question

If we add 1 in the numerator of a fraction and subtract 1 from its denominator, the fraction becomes 1, It is also given that the fraction becomes 1/2 when we add 1 to its denominator, and then what is the fraction.

Answer 1

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

If 1 is added to the numerator and 1 is subtracted from the denominator, the fraction becomes 1. Thus, we have

$\frac{x + 1}{y - 1} = 1 \\ = > x + 1 = y - 1 \\ = > x + 1 - y + 1 = 0\\ = > x - y + 2 = 0$


If 1 is added to the denominator, the fraction becomes 1/2. Thus, we have

$\frac{x}{y + 1} = \frac{1}{2} \\ = > 2x = y + 1 \\ = > 2x - y - 1 = 0$


So, we have two equations

$x - y + 2 = 0 \\ \\ 2x - y - 1 = 0$




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

By using cross-multiplication, we have

$\frac{x}{( - 1) \times ( - 1) - ( - 1) \times 2} = \frac{ - y}{1 \times ( - 1) - 2 \times 2} = \frac{1}{1 \times ( - 1) - - 2 \times ( - 1)} \\ \\ = > \frac{x}{1 + 2} = \frac{ - y}{ - 1 - 4} = \frac{1}{ - 1 + 2} \\ \\ = > \frac{x}{3} = \frac{ - y}{ - 5} = \frac{1}{1} \\ \\ = > \frac{x}{3} = \frac{y}{5} = 1 \\ \\ x = 3 \: \: . \: \: \: y = 5$




Hence, the fraction is 3/5.

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