Complete Math Formulas Guide: Percentage, Profit & Loss, Interest, Time, Work, Speed and Geometry
Mathematics formulas are the foundation of numerical problem-solving. Whether you are a school student preparing for board examinations or an aspirant preparing for competitive examinations such as TET, CTET, SSC, Railway, banking examinations and CGPSC, understanding important formulas can make calculations faster and more accurate.
This complete mathematics formulas guide explains important arithmetic and geometry formulas in simple language with examples. It is designed as a quick revision resource for students and competitive-exam aspirants.
- 1. Percentage, Profit and Loss
- 2. Simple and Compound Interest
- 3. Average and Ratio
- 4. Time and Work
- 5. Speed, Distance and Time
- 6. Basic Geometry Formulas
- 7. Important Mathematical Conversions
- 8. Exam Preparation Tips
- 9. Frequently Asked Questions
1. Percentage, Profit and Loss
Percentage means a number expressed as a fraction of 100. Profit and loss are commonly used in commercial mathematics to determine the gain or loss made in a transaction.
Important Percentage Formulas
| Concept | Formula | Example |
|---|---|---|
| Percentage | (Value ÷ Total Value) × 100 | (40 ÷ 50) × 100 = 80% |
| Profit | SP − CP | SP = ₹120, CP = ₹100, Profit = ₹20 |
| Loss | CP − SP | CP = ₹100, SP = ₹80, Loss = ₹20 |
| Profit % | (Profit ÷ CP) × 100 | (20 ÷ 100) × 100 = 20% |
| Loss % | (Loss ÷ CP) × 100 | (20 ÷ 100) × 100 = 20% |
| Discount | Marked Price − Selling Price | MP = ₹500, SP = ₹450, Discount = ₹50 |
| Discount % | (Discount ÷ Marked Price) × 100 | (50 ÷ 500) × 100 = 10% |
Profit percentage and loss percentage are normally calculated on the Cost Price (CP), not on the Selling Price (SP).
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2. Simple and Compound Interest
Interest is the amount paid or earned for the use of money. Simple Interest is calculated only on the principal amount, while Compound Interest is calculated on the principal plus the accumulated interest.
Simple Interest Formula
Where:
- P = Principal
- R = Rate of interest per year
- T = Time in years
Compound Interest Formulas
Here, A represents the final amount and P represents the principal.
Simple Interest is calculated on the original principal, whereas Compound Interest also considers previously accumulated interest.
3. Average and Ratio
Average
Average is obtained by dividing the sum of all observations by the total number of observations.
Example: The average of 2, 4 and 6 is: (2 + 4 + 6) ÷ 3 = 4.
Ratio
Ratio is used to compare two quantities of the same kind.
Example: If there are 20 boys and 10 girls, their ratio is 20 : 10 = 2 : 1.
4. Time and Work
Time and Work problems are commonly asked in competitive examinations. These questions are based on the relationship between the amount of work, the time taken and the efficiency of workers.
For example, if a person completes a task in 5 days, then the work completed in one day is 1/5.
Basic Work Formula
Questions involving two or more workers frequently use the concept of combined efficiency. In general, if more workers with the same efficiency are added, the time required to complete the same amount of work decreases.
5. Speed, Distance and Time
Speed, distance and time are closely related. Knowing any two of these quantities allows you to calculate the third.
Quick Memory Trick
Imagine a triangle with Distance (D) at the top and Speed (S) and Time (T) at the bottom.
Therefore: D = S × T, S = D ÷ T, and T = D ÷ S.
6. Basic Geometry Formulas
Geometry deals with shapes, sizes, lengths, areas, angles and properties of space. The following formulas are useful for school examinations and competitive exams.
| Shape | Formula |
|---|---|
| Rectangle Area | Length × Breadth |
| Rectangle Perimeter | 2 × (Length + Breadth) |
| Square Area | Side2 |
| Square Perimeter | 4 × Side |
| Triangle Area | 1/2 × Base × Height |
| Circle Area | ╧А × r2 |
| Circle Circumference | 2 × ╧А × r |
| Cube Volume | Side3 |
| Cuboid Volume | Length × Breadth × Height |
For many school-level calculations, the value of ╧А may be taken as 22/7 or 3.14, depending on the question.
7. Important Mathematical Conversions
| Conversion | Formula |
|---|---|
| km/h to m/s | Multiply by 5/18 |
| m/s to km/h | Multiply by 18/5 |
| 1 kilometre | 1000 metres |
| 1 metre | 100 centimetres |
| 1 hour | 60 minutes |
| 1 minute | 60 seconds |
8. Mathematics Exam Preparation Tips
Memorising formulas is useful, but applying them correctly is even more important. Use the following approach for better preparation:
- Understand the meaning of each formula before memorising it.
- Maintain a separate formula notebook for quick revision.
- Practise calculation-based questions regularly.
- Solve previous-year question papers to understand question patterns.
- Pay attention to units such as kilometres, metres, hours and seconds.
- Check calculations before submitting your answer.
- Practise percentage, ratio, average, time and work regularly for competitive examinations.
Questions may combine two or more concepts. For example, a single problem can involve percentage, ratio and profit and loss together. Therefore, do not learn formulas in isolation; practise applying them in different situations.
9. Frequently Asked Questions (FAQs)
Q1. What is the basic formula for percentage?
Percentage = (Value ÷ Total Value) × 100.
Q2. On which value is profit percentage calculated?
Profit percentage is normally calculated on the Cost Price (CP). Profit % = (Profit ÷ CP) × 100.
Q3. What is the formula for Simple Interest?
Simple Interest = (P × R × T) ÷ 100.
Q4. What is the relationship between speed, distance and time?
Distance = Speed × Time, Speed = Distance ÷ Time, and Time = Distance ÷ Speed.
Q5. How do you convert km/h into m/s?
Multiply the speed in km/h by 5/18 to convert it into m/s.
Q6. What is the difference between area and perimeter?
Area represents the space covered inside a two-dimensional shape, while perimeter represents the total length of its boundary.
Q7. Are these formulas enough for competitive examinations?
These formulas provide a strong foundation for basic mathematics. Competitive examinations may require additional formulas and concepts, as well as the ability to combine multiple concepts in a single problem.
Conclusion
Mathematics becomes easier when formulas are understood and practised regularly. The formulas in this guide cover several important topics, including percentage, profit and loss, simple and compound interest, average, ratio, time and work, speed, distance, time and basic geometry.
Students and competitive-exam aspirants should revise these formulas regularly and solve practice questions to improve speed, accuracy and confidence.
Practice makes calculation faster and more accurate. Revise these formulas regularly and apply them to previous-year questions and practice problems.