Arithmetic is an important part of Mathematics that covers practical topics such as Profit and Loss, Discount, VAT, Simple Interest, Population Growth, and Depreciation. These topics involve applying mathematical formulas and calculations to solve problems involving percentages, interest, price changes, population changes, and depreciation.
For Officer Cadet Entrance Exam preparation, arithmetic questions help develop calculation skills and the ability to apply formulas accurately and efficiently. This resource covers essential maths formulas, solving methods, useful tricks, and practice questions related to Profit and Loss, Discount, VAT, Simple Interest, Population Growth, and Depreciation. Explore the complete Officer Cadet Exam resources and Maths for Officer Cadet for additional practice and study materials.
What is Arithmetic?
Arithmetic is a branch of Mathematics that deals with numbers and the basic operations on them — addition, subtraction, multiplication, and division. In the context of the Officer Cadet Entrance Exam, arithmetic refers to the applied, calculation-based topics such as Profit and Loss, Discount, VAT, Simple Interest, Population Growth, and Depreciation.
These topics involve applying mathematical formulas and calculations to solve problems involving percentages, interest, price changes, population changes, and depreciation.
Example: If a shopkeeper buys an article for Rs. 500 and sells it for Rs. 600, the profit is Rs. 100, and the profit percent is 20%.
Arithmetic for Officer Cadet: Syllabus
This Mathematics for Officer Cadet Entrance Exam Preparation resource covers the following main topics:
1. Profit and Loss
2. Discount and VAT
3. Simple Interest
4. Population growth and Depreciation
1. Profit and Loss
Profit and Loss is one of the most frequently asked arithmetic topics in the Officer Cadet Entrance Exam. It deals with the cost price, selling price, profit, loss, and their percentages.
Key Formulas
| Term | Formula |
|---|---|
| Profit | Profit = SP − CP |
| Loss | Loss = CP − SP |
| Profit Percent | Profit % = (Profit / CP) × 100 |
| Loss Percent | Loss % = (Loss / CP) × 100 |
| Selling Price (Profit) | SP = CP × (100 + Profit%) / 100 |
| Selling Price (Loss) | SP = CP × (100 − Loss%) / 100 |
| Cost Price (Profit) | CP = SP × 100 / (100 + Profit%) |
| Cost Price (Loss) | CP = SP × 100 / (100 − Loss%) |
Where:
👉 CP = Cost Price
👉 SP = Selling Price
Example:
A man buys a watch for Rs. 800 and sells it for Rs. 920. Find his profit percent.
Solution:
CP = Rs. 800, SP = Rs. 920
Profit = SP − CP = 920 − 800 = Rs. 120
Profit % = (120 / 800) × 100 = 15%
Therefore, the profit percent is 15%.
2. Discount and VAT
Discount is the reduction given on the marked price of an article. VAT (Value Added Tax) is a tax added to the price of goods and services.
Key Formulas
| Term | Formula |
|---|---|
| Discount | Discount = MP − SP |
| Discount Percent | Discount % = (Discount / MP) × 100 |
| Selling Price after Discount | SP = MP × (100 − Discount%) / 100 |
| Marked Price | MP = SP × 100 / (100 − Discount%) |
| VAT Amount | VAT = SP × VAT% / 100 |
| Price with VAT | Price with VAT = SP + VAT |
Where:
👉 MP = Marked Price
👉 SP = Selling Price
Example
The marked price of a bag is Rs. 2,000. A discount of 15% is given, and 13% VAT is added. Find the final price paid by the customer.
Solution:
MP = Rs. 2,000
SP = 2000 × (100 − 15) / 100 = 2000 × 85 / 100 = Rs. 1,700
VAT = 1700 × 13 / 100 = Rs. 221
Final Price = SP + VAT = 1700 + 221 = Rs. 1,921
Therefore, the customer pays Rs. 1,921.
3. Simple Interest
Simple Interest is the interest calculated on the original principal for a fixed period at a fixed rate.
Key Formulas
| Term | Formula |
|---|---|
| Simple Interest | SI = (P × T × R) / 100 |
| Principal | P = (SI × 100) / (T × R) |
| Rate | R = (SI × 100) / (P × T) |
| Time | T = (SI × 100) / (P × R) |
| Amount | A = P + SI |
Where:
👉 P = Principal
👉 T = Time (in years)
👉 R = Rate of interest per annum
👉 A = Amount
Example
Find the simple interest on Rs. 5,000 at 8% per annum for 3 years.
Solution:
P = Rs. 5,000, R = 8%, T = 3 years
SI = (5000 × 3 × 8) / 100 = Rs. 1,200
Therefore, the simple interest is Rs. 1,200, and the amount is Rs. 6,200.
4. Population Growth and Depreciation
Population growth and depreciation are applications of percentage change over time. Population growth follows compound interest–type growth, while depreciation follows compound interest–type decrease.
Key Formulas
| Term | Formula |
|---|---|
| Population after T years | P_T = P₀ × (1 + R/100)^T |
| Population before T years | P₀ = P_T / (1 + R/100)^T |
| Depreciated Value after T years | V_T = V₀ × (1 − R/100)^T |
| Original Value before T years | V₀ = V_T / (1 − R/100)^T |
Where:
👉 P₀ = Initial population
👉 P_T = Population after T years
👉 V₀ = Initial value
👉 V_T = Value after T years
👉 R = Rate of growth or depreciation
👉 T = Time in years
Example
The population of a town is 50,000. If it grows at 2% per annum, find the population after 2 years.
Solution:
P₀ = 50,000, R = 2%, T = 2 years
P_T = 50000 × (1 + 2/100)²
= 50000 × (1.02)²
= 50000 × 1.0404
= 52,020
Therefore, the population after 2 years is 52,020.
Effective Tricks to Solve Arithmetic Questions
These tricks will help you solve arithmetic questions quickly and accurately in the Officer Cadet Entrance Exam.
Trick 1: Use Fraction Equivalents for Percentages
Convert common percentages into fractions to speed up calculations:
👉 10% = 1/10, 20% = 1/5, 25% = 1/4, 50% = 1/2, 12.5% = 1/8, 16.66% = 1/6
Trick 2: Use the Multiplier Method
Instead of calculating profit or discount separately, use a single multiplier:
👉 For 20% profit: SP = CP × 1.20
👉 For 15% discount: SP = MP × 0.85
👉 For 13% VAT: Price with VAT = SP × 1.13
Trick 3: Assume a Convenient Value
When the actual value is not given, assume a convenient number such as 100 or the LCM of the given values. This simplifies percentage-based problems.
Trick 4: Use the Successive Percentage Formula
For two successive changes of a% and b%:
👉 Net change % = a + b + (ab / 100)
Example: 10% increase followed by 10% decrease = 10 − 10 − (100/100) = −1% (a net decrease of 1%).
Trick 5: Remember the CP–SP Relationship
👉 If an article is sold at a profit of x%, then SP = CP × (100 + x)/100
👉 If sold at a loss of x%, then SP = CP × (100 − x)/100
Memorizing these avoids repeated formula derivation.
Trick 6: For Depreciation, Use the Same Compound Formula
Depreciation is just compound decay. Use V_T = V₀ × (1 − R/100)^T and treat it exactly like compound interest with a negative rate.
Important Tips to Solve Arithmetic Questions
👉 Memorize the formulas — Profit and Loss, Discount, VAT, Simple Interest, Population Growth, and Depreciation formulas should be at your fingertips.
👉 Practise percentage-to-fraction conversions — This alone can cut calculation time significantly.
👉 Read the question carefully — Identify whether it asks for profit/loss percent, SP, CP, MP, VAT amount, or final price.
👉 Draw a quick table — For multi-step problems, organize given values in a table before solving.
👉 Double-check units — Ensure time is in years, rate is per annum, and currency units are consistent.
👉 Time yourself — Practice under exam conditions to improve speed and accuracy.
Practice Questions
- A man buys a cycle for Rs. 1,200 and sells it for Rs. 1,380. Find his profit percent.
- The marked price of a mobile is Rs. 15,000. A discount of 10% is given, and 13% VAT is added. Find the final price paid by the customer.
- Find the simple interest on Rs. 8,000 at 6% per annum for 2 years.
- The population of a village is 25,000. If it grows at 4% per annum, find the population after 2 years.
- The value of a machine depreciates at 10% per annum. If its present value is Rs. 50,000, find its value after 2 years.
- A shopkeeper sells an article at a loss of 12%. If the cost price is Rs. 2,500, find the selling price.
- If the simple interest on a sum for 3 years at 5% per annum is Rs. 900, find the principal.
- After a 20% discount, the selling price of a shirt is Rs. 640. Find the marked price.
- The population of a town is 40,000. If it decreases at 5% per annum, find the population after 2 years.
- A man sells two articles at Rs. 1,000 each, one at a profit of 10% and the other at a loss of 10%. Find his overall profit or loss percent.
Conclusion
Arithmetic is an important part of the Mathematics syllabus for Officer Cadet Entrance Exam preparation. Topics such as Profit and Loss, Discount, VAT, Simple Interest, Population Growth, and Depreciation are highly scoring once you understand the underlying formulas and the relationships between the given quantities.
Focus on the key formulas, learn to convert percentages into fractions and multipliers, and practice applying the correct formula to the correct situation. With regular practice, arithmetic questions can become a quick-scoring area in the mathematics section.
This resource is part of the Officer Cadet Entrance Exam Preparation series, focusing on Maths for Officer Cadet Entrance Exam. For structured lessons, comprehensive practice question banks, and mock tests, explore the Arithmetic for Officer Cadet section of the Maths for Officer Cadet Entrance Exam course on the Pratima Academy LMS.