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
Let us consider that fraction is = \(\frac{A}{B}\)
A + B = 11 ----(1)
ATQ,
\(\frac{A + 1 }{B - 2 }\) = \(\frac{2}{3}\)
3A + 3 = 2B - 4
3A - 2B = -7 -----(2)
Multiply equation 1 by 2 and add equation 1 and 2 ,
2A + 3A = -7 + 22
5A = 15
A = 3
Put A in equation 1 ,
3 + B = 11
B = 8
So, The fraction = \(\frac{3}{8}\)
The correct answer is Option (3) → $\frac{3}{8}$