question_answer

  A fraction becomes \[\text{4}/\text{5}\] when 1 is added to each of the numerator and denominator. However, if we subtract 5 from each of them, it becomes \[\text{1}/\text{2}\]. Then, numerator of the fraction is:

A) 6

B) 7

C) 8

D) 9

Correct Answer: B

Solution :

[b] Let the fraction be \[\frac{x}{y}\]

Then, according to question,

\[\frac{x+1}{y+1}=\frac{4}{5}\,\,\,\Rightarrow \,\,\,5x+5=4y+4\]

\[5x-4y=-1\]                   (1)

and       \[\frac{x-5}{y-5}=\frac{1}{2}\]

\[2x-10=y-5\]

\[2x-y=5\]                  ...(2)

On multiplying eq. (1) by 2 and eq. (2) by 5 and then subtracting eq. (2) from eq. (1), we get

\[y=9\]

Substituting the value of y in eq. (1), we get

\[5x-4\times 9=-1\]

\[5x=-1+36\,\,\,\Rightarrow x=7\]

Hence,   Fraction \[=\frac{7}{9}\]

Therefore, numerator of this fraction is 7.