The sum of the numerator and the denominator of a fraction is 11. If 1 is added to the numerator and 2 is subtracted from the denominator, it becomes \(\frac{2}{3}\). The fraction is:
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → \(\frac{3}{8}\)
Let the fraction be \(\frac{x}{y}\). Each condition in the question gives one equation; the two are then solved together.
The sum of the numerator and the denominator: \(x+y=11\) (1)
The changed fraction: \(\displaystyle\frac{x+1}{y-2}=\frac{2}{3}\)
\(3x+3=2y-4\)
\(3x-2y=-7\) (2)
From (1), \(y=11-x\); putting this in (2): \(3x-22+2x=-7\)
\(5x=15\), so \(x=3\) and \(y=8\): the fraction is \(\frac{3}{8}\)