A) \[\frac{1}{2}\]
B) \[\frac{4}{13}\]
C) \[\frac{3}{10}\]
D) \[\frac{2}{7}\]
Correct Answer: C
Solution :
Case I Let the numerator be x then denominator \[=3x+1\] \[\therefore \] Fraction \[=\frac{x}{3x+1}\] Case II New numerator = x + 1 New denominator \[=3x+1-2\] New fraction \[=\frac{x+1}{3x-1}\] Given \[\frac{x+1}{3x-1}=0.5\] \[\frac{x+1}{3x-1}\,=\frac{5}{10}\] \[\frac{x+1}{3x-1}=\frac{1}{2}\] \[2(x+1)=3x-1\] \[2x+2=3x-1\] \[2x-3x=-1-2\] \[-x=-3\] \[x=3\] \[\therefore \] Original fraction\[=\frac{3}{3\times 3+1}\,=\frac{3}{10}\]
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