Question

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

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

Answer 1

Answer: (D)

$a\ast b=\frac{ab}{10},5\ast 8=\frac{5\cdot 8}{10}=4$
Now identity element of $4$ is $4\ast e=4=e\ast 4$
$\Rightarrow \frac{4\cdot e}{10}=4=\frac{e\cdot 4}{10}$
$\Rightarrow e=10$
Now, inverse element of $4$ is $4\ast b=e=b\ast 4$
$\Rightarrow \frac{4b}{10}=10=\frac{b4}{10}$
$\Rightarrow b=25$