A number is larger than half of 100. It is more than 6 tens and less than 8 tens. The sum of its digits is 9. The tens digit is the double of the ones digit. What is the number ?

The correct option is 63.

Let's solve the problem step-by-step using the given clues:

1. "A number is larger than half of 100."
Half of 100 is equal to:
$\frac{100}{2}=50$
So, the number must be greater than 50.

2. "It is more than 6 tens and less than 8 tens."
6 tens = 60
8 tens = 80
So, the number is strictly between 60 and 80. This means the tens digit must be either 6 or 7.

3. "The tens digit is the double of the ones digit."
Let the tens digit be $t$ and the ones digit be $o$.
We are given that $t=2\times o$.
Since $t$ can only be 6 or 7:
- If $t=6$, then $o=\frac{6}{2}=3$. This gives the number 63.
- If $t=7$, $o$ would not be a whole number ($72=3.5$), which is invalid for a digit.

4. "The sum of its digits is 9."
Let's verify this for 63:
$6+3=9$
This condition is also satisfied.

Therefore, the number is 63.