| The numerator of a fraction is 4 less than its denominator. If the numerator is decreased by 2 and the denominator is increased by 1, then the denominator becomes eight times the numerator. Find the fraction. [SSC (CGL) 2013] |
A) \[\frac{3}{7}\]
B) \[\frac{4}{7}\]
C) \[\frac{5}{7}\]
D) \[\frac{6}{7}\]
Correct Answer: A
Solution :
| Let denominator of fraction \[=x\] |
| Then, numerator \[=x-4\] |
| \[\therefore \]Fraction \[=\frac{x-4}{x}\] |
| According to the question, |
| \[\frac{(x-4)-2}{x+1}=\frac{1}{8}\] |
| \[\Rightarrow \] \[x-6=\frac{x+1}{8}\] |
| \[\Rightarrow \] \[8x-48=x+1\] |
| \[\Rightarrow \] \[8x-x=48+1\] |
| \[\Rightarrow \] \[7x=49\]\[\Rightarrow \]\[x=7\] |
| \[\therefore \]Fraction \[=\frac{7-4}{7}=\frac{3}{7}\] |
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