Question

If $a* b=\frac{a b}{10} ; a, b \in Q^{+}$, then $(5 * 8)^{-1}=$ ___________

• A. 4
• B. $\frac{1}{25}$
• C. 10
• D. 25

Answer 1

Answer: (D)

$a * b =\frac{a b}{10}, 5* 8=\frac{5 \cdot 8}{10}=4$
Now identity element of $4$ is $4* e=4=e* 4$
$ \Rightarrow \frac{4 \cdot e}{10}=4=\frac{e \cdot 4}{10} $
$\Rightarrow e=10$
Now, inverse element of $4$ is $4* b = e = b * 4 $
$\Rightarrow \frac{4 b}{10}=10=\frac{b 4}{10}$
$ \Rightarrow b =25$