A) \[5x-4y+2=0,x-y=0\]
B) \[5x-4y+2=0,2x-y-4=0\]
C) \[x+4y=0,y+2x=0\]
D) None of the above
Correct Answer: B
Solution :
Let the numerator of the fraction be x and denominator be y. |
Then, the fraction is \[\frac{x}{y}\]. Now, according to condition I, we have |
\[\frac{x+2}{y+2}=\frac{4}{5}\] |
\[\Rightarrow \,\,\,5x+10=4y+8\] |
[cross-multiply both sides] |
\[\Rightarrow \,\,\,\,5x-4y+2=0\] ...(i) |
and according to condition II, we have |
\[\frac{x-4}{y-4}=\frac{1}{2}\] |
[cross-multiply both sides] |
\[\Rightarrow \,\,\,2x-8=y-4\] |
\[\Rightarrow \,\,\,\,2x-y-4=0\] ...(ii) |
Thus, the algebraic representation of given problem is |
\[5x-4y+2=0\] |
and \[2x-y-4=0\] |
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