If we add 1 to the numerator and subtract 1 from the

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Question 1:-  If we add 1 to the numerator and subtract 1 from the denominator, a fraction becomes 1. It also becomes 1/2 if we add 1 to the denominator. What is the fraction.

Solution:- Let the fraction = \dfrac{x}{y}

Then, according to the first condition, we have

\dfrac{x+1}{y-1} = 1

\Rightarrow x + 1 = y - 1

\Rightarrow x - y = -2 ……..(i)

According to the second condition

\dfrac{x}{y + 1} = \dfrac{1}{2}

\Rightarrow 2x = y + 1

\Rightarrow 2x - y = 1 …….(ii)

Subtracting eq (i) to eq (ii)

(x - y)-(2x - y) = -2 - 1

\Rightarrow x - y - 2x + y = -3

\Rightarrow -x = -3

\Rightarrow x = 3

Putting the value of x in (i)

x - y = -2

\Rightarrow 3 - y = -2

\Rightarrow 3 + 2 = y

\Rightarrow y = 5

Hence, the fraction =\dfrac{3}{5}

Some other question

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2: find the value of k for which the pair of equation

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