Question : The numerator of a fraction is 6 less than its denominator. If the numerator is decreased by 1 and the denominator is increased by 5, then the denominator becomes 4 times the numerator. Find the fraction.
Option 1: $\frac{5}{11}$
Option 2: $\frac{3}{11}$
Option 3: $\frac{4}{11}$
Option 4: $\frac{7}{11}$
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Correct Answer: $\frac{5}{11}$
Solution :
Let the numerator of the fraction be '$x$' and the denominator = $x$ + 6
According to the question,
⇒ 4 × ($x$ - 1) = ($x$ + 6) + 5
⇒ 4$x$ - 4 = $x$ + 11
⇒ $x$ = 5
So, The numerator of the fraction = 5
and the denominator of the fraction = $x$ + 6
= 5 + 6
= 11
$\therefore$ the original fraction is $\frac{5}{11}$
Hence, the correct answer is $\frac{5}{11}$.
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