A) \[\frac{5}{12}\]
B) \[\frac{7}{23}\]
C) \[\frac{1}{8}\]
D) \[\frac{2}{3}\]
Correct Answer: C
Solution :
[c] Let the numerator and denominator of a fraction are x and y, respectively, According to question, \[\frac{x-\,1}{y}=\frac{1}{3}\Rightarrow \,\,\,3x-\,3=y\Rightarrow \,\,\,3x-\,y=3...(i)\] And \[\frac{x}{y+5}=\frac{1}{4}\Rightarrow \,\,\,4x-\,y=5\,\,\,\,\,\,\,\,...(ii)\] On solving eqs. (i) and (ii), we get \[x=2\,\,\,and\,\,\,y=3\] \[\therefore \] Required fraction .\[=\frac{x-1}{y+5}=\frac{2-1}{3+5}=\frac{1}{8}\]
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