Jane is 25 years old.  Dick is older than Jane.  In $n$ years, where $n$ is a positive integer, Dick's age and Jane's age will both be two-digit number and will have the property that Jane's age is obtained by interchanging the digits of Dick's age.  Let $d$ be Dick's present age.  How many ordered pairs of positive integers $(d,n)$ are possible?
1. Let \( d \) be Dick's current age and \( n \) be the number of years in the future. In \( n \) years, Dick's age will be \( d + n \) and Jane's age will be \( 25 + n \).
2. Let \( D = d + n \) and \( J = 25 + n \). Since \( D \) and \( J \) are two-digit numbers, we can express them as \( D = 10x + y \) and \( J = 10y + x \), where \( x \) and \( y \) are digits.
3. We have the equations:
   \[
   D = 10x + y = d + n
   \]
   \[
   J = 10y + x = 25 + n
   \]
4. Subtract the second equation from the first:
   \[
   10x + y - (10y + x) = d + n - (25 + n)
   \]
   \[
   9x - 9y = d - 25
   \]
   \[
   9(x - y) = d - 25
   \]
   \[
   d - 25 = 9(x - y)
   \]
   \[
   d \equiv 7 \pmod{9}
   \]
5. The possible values for \( d \) that satisfy \( d \equiv 7 \pmod{9} \) and are two-digit numbers are: 34, 43, 52, 61, 70, 79, 88, and 97.
6. For each value of \( d \), we need to find the corresponding values of \( n \) such that \( 10x + y = d + n \) and \( 10y + x = 25 + n \).

   - If \( d = 34 \):
     \[
     9(x - y) = 34 - 25 = 9 \implies x - y = 1
     \]
     \[
     10x + y = 34 + n
     \]
     Possible values for \( 10x + y \) are 43, 54, 65, 76, 87, and 98. These yield \( n = 9, 20, 31, 42, 53, 64 \) respectively. (6 possibilities)

   - If \( d = 43 \):
     \[
     9(x - y) = 43 - 25 = 18 \implies x - y = 2
     \]
     \[
     10x + y = 43 + n
     \]
     Possible values for \( 10x + y \) are 53, 64, 75, 86, and 97. These yield \( n = 10, 21, 32, 43, 54 \) respectively. (5 possibilities)

   - If \( d = 52 \):
     \[
     9(x - y) = 52 - 25 = 27 \implies x - y = 3
     \]
     \[
     10x + y = 52 + n
     \]
     Possible values for \( 10x + y \) are 63, 74, 85, and 96. These yield \( n = 11, 22, 33, 44 \) respectively. (4 possibilities)

   - If \( d = 61 \):
     \[
     9(x - y) = 61 - 25 = 36 \implies x - y = 4
     \]
     \[
     10x + y = 61 + n
     \]
     Possible values for \( 10x + y \) are 62, 73, 84, and 95. These yield \( n = 1, 12, 23, 34 \) respectively. (4 possibilities)

   - If \( d = 70 \):
     \[
     9(x - y) = 70 - 25 = 45 \implies x - y = 5
     \]
     \[
     10x + y = 70 + n
     \]
     Possible values for \( 10x + y \) are 72, 83, and 94. These yield \( n = 2, 13, 24 \) respectively. (3 possibilities)

   - If \( d = 79 \):
     \[
     9(x - y) = 79 - 25 = 54 \implies x - y = 6
     \]
     \[
     10x + y = 79 + n
     \]
     Possible values for \( 10x + y \) are 82 and 93. These yield \( n = 3, 14 \) respectively. (2 possibilities)

   - If \( d = 88 \):
     \[
     9(x - y) = 88 - 25 = 63 \implies x - y = 7
     \]
     \[
     10x + y = 88 + n
     \]
     The only possible value for \( 10x + y \) is 92. This yields \( n = 4 \). (1 possibility)

7. Summing all the possibilities:
   \[
   6 + 5 + 4 + 4 + 3 + 2 + 1 = \frac{6 \cdot 7}{2} + 4 = 25
   \]

The final answer is \(\boxed{25}\)