question_answer

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

A) 6

B) 7

C) 8

D) 9

Correct Answer: B

Solution :

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

Then, according to the question

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

\[\Rightarrow \,\,\,\,\,\,\,5x+5=4y+4\]

\[\Rightarrow \,\,5x-4y=-1\]                      (i)

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

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

\[\Rightarrow \,\,\,\,2x-y=5\]                                 (ii)

On multiplying Eq. (i) by 2 and Eq. (ii) by 5 and then subtracting Eq. (ii) from Eq. (i), we get

\[10x-8y=-2\]

On substituting the value of y in Eq. (i), we get

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

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

\[\Rightarrow \,\,\,\,x=7\]

\[\therefore \] Fraction \[=\frac{7}{9}\]

Therefore, numerator of this fraction is 7.