There are several techniques that can help improve speed while solving numerical problems in previous years' papers of UPSC Management optional subject. These techniques focus on enhancing mathematical proficiency and efficiency, as well as adopting strategic approaches to problem-solving. Below are some key techniques to consider:

1. Familiarize Yourself with the Syllabus
- Thoroughly understanding the syllabus is crucial for effective preparation. Identify the specific topics and subtopics covered in the previous years' papers and allocate sufficient time for each.

2. Master the Fundamentals
- Strengthen your foundation by revising basic mathematical concepts, formulas, and shortcuts. Familiarize yourself with various numerical methods, statistical techniques, and mathematical models relevant to the management field.

3. Practice Regularly
- Consistent practice is essential for increasing speed and accuracy. Regularly solve numerical problems from previous years' papers and other relevant resources. Set aside dedicated practice sessions to hone your problem-solving skills.

4. Time Management
- Develop effective time management strategies to ensure efficient utilization of time during the exam. Allocate appropriate time to each question based on its difficulty level. Avoid spending excessive time on any one question, as it may hinder progress on other questions.

5. Understand the Question
- Read each question carefully to grasp its requirements. Identify the given data, required calculations, and any specific instructions provided. This ensures a clear understanding of the problem and prevents unnecessary errors.

6. Work Backwards
- In some cases, working backwards can save time. Start with the answer choices and evaluate whether they satisfy the given conditions. This technique can help eliminate incorrect options quickly and narrow down the possible solutions.

7. Utilize Approximations
- Use approximation techniques to simplify complex calculations, especially when the answer choices have a significant difference. Rounding off numbers and using approximations can help reduce the computation time while maintaining reasonable accuracy.

8. Solve Simpler Parts First
- Break down complex problems into simpler parts and solve them individually. By solving easier sub-problems first, you gain confidence and save time. Once the simpler parts are completed, proceed to the more challenging aspects.

9. Develop Speed Math Techniques
- Familiarize yourself with various speed math techniques such as mental calculations, shortcut formulas, and pattern recognition. These techniques can significantly reduce the time required for calculations and improve overall speed.

10. Analyze Mistakes
- Review your mistakes and weaknesses regularly. Identify common errors and areas where you tend to spend more time. By addressing these issues, you can gradually improve your speed and accuracy.

In summary, improving speed while solving numerical problems in the previous years' papers of UPSC Management optional subject requires a combination of strong mathematical fundamentals, regular practice, efficient time management, and strategic problem-solving techniques. By following these techniques and consistently working towards enhancing your skills, you can increase your speed and perform better in the exam.