A) \[4:5\]
B) \[3:2\]
C) \[4:1\]
D) \[3:1\]
Correct Answer: C
Solution :
[c] |
\[A.T.Q\,\,\,x+3+y+z=9+6-y+z+4-x\] |
\[\Rightarrow \,\,\,\,\,\,\,\,\,\,\,\,\,\,x+3+y=19-x-y\] |
\[\Rightarrow \,\,\,\,\,\,\,\,\,\,\,\,\,\,2x+2y=16\] |
\[\Rightarrow \,\,\,\,\,\,\,\,\,\,\,\,\,\,x+y=8\] |
\[\Rightarrow \,\,\,\,\,\,\,\,\,\,\,\,\,\,y=8-x\] |
Also \[\frac{x}{4-x}=\frac{y}{6-y}\] |
\[\Rightarrow \,\,\,\,\,\,\,\,\,\,\,\,\,\,\frac{x}{4-x}=\frac{8-x}{6-8+x}\] |
\[\Rightarrow \,\,\,\,\,\,\,\,\,\,\,\,\,\,x(x-2)=(8-x)\,\,(4-x)\] |
\[\Rightarrow \,\,\,\,\,\,\,\,\,\,\,\,\,\,{{x}^{2}}-2x=32-12x+{{x}^{2}}\] |
\[\Rightarrow \,\,\,\,\,\,\,\,\,\,\,\,\,\,x=3.2cm\] |
\[\therefore \] Ratio \[=\frac{3.2}{4-3.2}=\frac{4}{1}\] |
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