There are several techniques and shortcuts that can help solve numerical problems quickly. These methods are particularly useful when attempting competitive exams like UPSC, where time is a crucial factor. Below are some effective strategies to improve speed and accuracy in solving numerical problems:

1. Familiarize Yourself with Basic Concepts:
Having a strong foundation in basic mathematical concepts is essential. Make sure you are well-versed in arithmetic operations, algebra, geometry, and trigonometry. This will enable you to quickly identify the appropriate method or formula to solve a problem.

2. Learn Mental Math Techniques:
Mental math techniques can significantly speed up calculations. Practice methods like estimation, rounding off, squaring numbers mentally, and finding square roots using approximation. This will allow you to quickly arrive at approximate answers, eliminating the need for lengthy calculations.

3. Memorize Important Formulas:
Memorizing important formulas and their derivations will save time during exams. Focus on formulas related to areas, volumes, trigonometry, and algebraic equations. By having them at the tip of your fingers, you won't waste time trying to recall or derive them.

4. Break Down Complex Problems:
Sometimes, numerical problems may appear complex at first glance. Break them down into smaller, manageable parts to simplify the calculations. This technique will help you identify the necessary steps and avoid getting overwhelmed by the complexity.

5. Solve Practice Questions:
Regularly solving practice questions is essential to improve your speed and accuracy. Identify the types of problems that frequently appear in exams and practice solving them under timed conditions. This will help you become familiar with the patterns and techniques required to solve them quickly.

6. Use Approximations and Elimination:
When multiple-choice options are available, use approximation techniques to quickly eliminate unlikely answers. By making rough estimates, you can narrow down the options and select the most plausible answer, saving time on detailed calculations.

7. Use Shortcut Techniques:
Learn shortcut techniques for specific types of problems. For example, using the cross-multiplication method for solving proportion problems or using the Vedic math technique for multiplication, division, and finding square roots. These methods are designed to simplify calculations and save time.

8. Time Management:
Lastly, time management plays a crucial role in solving numerical problems quickly. Allocate a specific amount of time to each question based on its complexity. If you find a problem too challenging, move on to the next one and come back to it later if time permits.

In conclusion, by mastering basic concepts, practicing mental math techniques, memorizing formulas, breaking down complex problems, solving practice questions, using approximations and shortcuts, and managing time effectively, you can greatly improve your speed and accuracy in solving numerical problems. Regular practice and familiarity with these techniques will help you excel in competitive exams like UPSC.