A) \[\frac{27}{20}\]
B) \[\frac{20}{27}\]
C) \[\frac{1}{20}\]
D) 20
Correct Answer: A
Solution :
Let e is the identity element of \[{{Q}^{+}}\] then, \[e*a=a,\,\forall \,a\in {{Q}^{+}}\] \[\frac{ea}{3}=a\] \[[\,\because \,a*b=\frac{ab}{3}]\] \[\therefore \] \[e=3\] Again, let b be die inverse of a then, \[a*b=e\] \[\frac{ab}{3}=3\,\,\,[\] \[[\because \,\,e=4]\] \[b=\frac{9}{a}\] \[\therefore \] Inverse of 4 is \[\frac{9}{4}\]. From the given condition, \[5*x={{4}^{-1}}\] \[\frac{5x}{3}=\frac{9}{4}\] \[\Rightarrow \] \[x=\frac{27}{20}\]You need to login to perform this action.
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