1998-1999 Algorithms Seminar By Bruno Salvy: A Research Report Overview.pdf

To solve the problem, we need to determine how many more years it will take for the age of B to be twice that of A. Let's break down the information given:

1. Current Ages:
- The ratio of ages of A and B is 3:5.
- Assume A's current age is \(3x\) and B's current age is \(5x\).

2. Age Difference:
- The difference in their ages is \(5x - 3x = 2x\).
- We know this difference is 10 years, so:
\[
2x = 10
\]
- Solving for \(x\), we get:
\[
x = 5
\]

3. Current Ages in Years:
- A's current age: \(3x = 3 \times 5 = 15\) years.
- B's current age: \(5x = 5 \times 5 = 25\) years.

4. Future Condition:
- We need to find when B's age will be twice that of A's age.
- Let the number of years from now be \(y\).
- In \(y\) years, A's age will be \(15 + y\) and B's age will be \(25 + y\).

5. Equation for Future Ages:
- We want B's future age to be twice A's future age:
\[
25 + y = 2(15 + y)
\]

6. Solve the Equation:
- Expand and simplify the equation:
\[
25 + y = 30 + 2y
\]
- Rearrange to solve for \(y\):
\[
25 + y - y = 30 + 2y - y
\]
\[
25 = 30 + y
\]
\[
25 - 30 = y
\]
\[
y = -5
\]

The negative result indicates that B was twice A's age 5 years ago.

7. Conclusion:
- Since the condition has already been met in the past, it will not occur again in the future.
- Therefore, the number of years from now when B's age will be twice A's age is \(\boxed{0}\).