Question 7
We say a rational number is funny if removing the same nonzero digit from both its numerator and denominator yields the same rational number as when it is properly simplified (not necessarily to lowest terms). For example,
is a funny rational number but
is not. Find the total number of funny rational numbers $\frac ab$ such that $10\le a\lt b\le99$.
is a funny rational number but
is not. Find the total number of funny rational numbers $\frac ab$ such that $10\le a\lt b\le99$.