If $73_x$ (in base-x number system) is equal to $54_y$ (in base $y$-number system), the possible values of $x$ and $y$ are
Answer is D.
$x\times 7 + 3 = 5 \times y + 4 \implies 7x = 5y + 1$.
Only option satisfying this is D.
I guess there are infinitely many solutions to this. (Not sure though. I don't know how to prove that there are infinitely many solutions. May be use mathematical induction?)
Some of the solutions are:
I just plotted the graph for 5y = 7x - 1 here - link to get these solutions
@rohith1001 Yes, there can be infinitely many solutions. The only conditons are that x > 7 and y > 5.