Which of the following numbers is divisible by both 9 and 43?

The correct option is 8901.

To determine which of the numbers is divisible by both 9 and 43, we can test the conditions for divisibility for each of the given options.

Step 1: Test for Divisibility by 9
A number is divisible by 9 if and only if the sum of its digits is divisible by 9.
Let us calculate the sum of the digits for each option:
- For 10710: $1+0+7+1+0=9$ (divisible by 9)
- For 8901: $8+9+0+1=18$ (divisible by 9)
- For 7230: $7+2+3+0=12$ (not divisible by 9)
- For 7095: $7+0+9+5=21$ (not divisible by 9)

This leaves us with two candidate numbers: 10710 and 8901.

Step 2: Test for Divisibility by 43
Now, we check which of the remaining numbers is divisible by 43 by performing direct division:

For 8901:
$\frac{8901}{43}=207$
Since the result is a whole number, 8901 is divisible by 43.

For 10710:
$\frac{10710}{43}\approx 249.07$
Since the result is not a whole number, 10710 is not divisible by 43.

Therefore, 8901 is the only number among the options that is divisible by both 9 and 43.