A) 0
B) 1
C) 2
D) 3
Correct Answer: B
Solution :
On adding giving equations, we get \[x+\{x\}\,=[x\}+y+[y]\,+\{y\}+z+[z]\] \[+[z]=13\] \[\Rightarrow \] \[2x+2y+2z=13\] \[(\because \,x=[x]+\{x\})\] \[\Rightarrow \] \[x+y+z=6.5\] Also, \[(x-\{x\})+(z-[z])=6.5-2.3\] \[\Rightarrow \] \[[x]+[z]=4.2\] \[\Rightarrow \] \[[x]=4,\,\,\{z\}=0.2\] Similarly, \[\{y\}+[z]=2\,\,\,\Rightarrow \,\,\,\{y\}=0,\,\,[z]=2\] Also, \[\{x\}+[y]=0.3\] \[\Rightarrow \] \[\{x\}=0.3\] and \[[y]=0\] \[\therefore \] \[x=[x]+[x]\,=4+0.3=4.3\] \[x=[y]\,+\{y\}\,=0+0=0\] \[z=[z]+\{z\}=2\,+0.2\,=2.2\] Hence, (4, 3, 0, 2, 2) is the only solution.You need to login to perform this action.
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