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If we add 1 to the numerator and subtract 1 from the denominator, a fraction reduces to 1. It becomes  \(\dfrac{1}{2}\) if we only add 1 to the denominator. What is the fraction?
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If we add 1 to the numerator and subtract 1 from the denominator, a fraction reduces to 1. It becomes  \(\dfrac{1}{2}\) if we only add 1 to the denominator. What is the fraction?

Answer

\(\frac{3}{5}\)
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Solution

Let the fraction be \(\frac ab\)
According to the given information,
\(\dfrac{a+1}{b-1}=1\)
\(a+1=b-1\)
\(a-b=2\)...(i)
Now, again, according to the question,
\(\dfrac{a}{b+1}\)=\(\dfrac{1}{2}\) 
\(2a=b+1\)
\(2a−b=1\)....(ii)
When equation (i) is subtracted from equation (ii) we get,
a= 3
When a = 3 is substituted in equation (i) we get,
3-b=-2
-b=-5
b = 5
Hence, the fraction is \(\frac{3}{5}\)
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