The Profit and Loss Test is a fundamental topic in Numerical Reasoning that evaluates your understanding of basic business transactions and your ability to calculate gains or losses in various scenarios. These questions test your grasp of cost price, selling price, profit percentage, loss percentage, discounts, and marked prices. The key skill is to quickly identify the relationship between cost price and selling price and apply the correct formula.
In this guide, we’ll explore what profit and loss problems involve, the key formulas you need, the common question types you’ll encounter, proven methods to solve them, and practical tricks to boost your speed and accuracy.
- What is Profit and Loss in Numerical Reasoning?
- What Skills Do These Questions Measure?
- Important Terms and Definitions
- Fundamental Formulas
- How to Solve Profit and Loss Questions
- Types of Profit and Loss Questions
- Finding Profit or Loss Percentage
- Finding Selling Price When Profit% is Given
- Finding Cost Price When SP and Profit% are Given
- Discount Problems
- Two Articles Sold at the Same Price
- Successive Profit or Loss
- Overall Profit Across Different Rates
- Important Tricks
- Trick 1: Use the Fraction Method
- Trick 2: Use Multiplication Factors
- Trick 3: Remember the Rule of Fractions
- Trick 4: For "No Profit, No Loss" with Two Articles
- Trick 5: Adjust Selling Price for a Different Profit Target
- Trick 6: Calculate 10% Quickly
- Trick 7: Calculate 5% Quickly
- Trick 8: Use the Unitary Method
- Common Mistakes to Avoid
- Quick Solving Checklist
- Practice Questions
- Conclusion
What is Profit and Loss in Numerical Reasoning?
Profit and Loss refers to calculating how much gain or loss is made in a transaction based on the Cost Price (CP) and Selling Price (SP) of a product. If the selling price is higher than the cost price, the difference is a profit; if it’s lower, the difference is a loss.
Example: A man buys an article for $500 and sells it for $600. Find his profit percentage. The profit is the difference between selling price and cost price, and expressing that as a share of the cost price gives the percentage. Answer: 20%
These problems are based on real-world business scenarios such as buying and selling goods, calculating profit margins, understanding discounts and offers, working out the true cost of items after a discount, and analyzing overall profit or loss across multiple transactions.
What Skills Do These Questions Measure?
Profit and loss questions test your ability in:
- Arithmetic calculation – working accurately with prices and percentages
- Understanding of percentages – converting between percentages, fractions, and multipliers
- Applying formulas quickly – matching the right formula to what’s given
- Logical reasoning in multi-step problems – chaining several calculations together correctly
- Speed and accuracy – solving under exam time pressure without careless errors
Profit and Loss is a high-scoring topic in the Numerical Reasoning section because questions follow predictable patterns with straightforward formulas. Common scenarios include basic profit/loss calculation, finding CP or SP from a given percentage, discount problems, successive profits or losses, overall profit or loss across multiple transactions, dishonest dealings involving false weights, and articles sold at the same price with different profit/loss percentages.
Important Terms and Definitions
- Cost Price (CP) – the price at which a product is bought or manufactured
- Selling Price (SP) – the price at which the product is sold
- Profit (or Gain) – the amount by which SP exceeds CP: Profit = SP − CP
- Loss – the amount by which CP exceeds SP: Loss = CP − SP
- Marked Price (MP) – the price printed on a product, also called the list price or MRP
- Discount – a reduction on the marked price: Discount = MP − SP
- Profit Percentage (Profit%) – profit expressed as a percentage of cost price: Profit% = (Profit ÷ CP) × 100
- Loss Percentage (Loss%) – loss expressed as a percentage of cost price: Loss% = (Loss ÷ CP) × 100
Fundamental Formulas
Basic Profit and Loss Formulas
| Quantity | Formula |
|---|---|
| Profit | SP − CP |
| Loss | CP − SP |
| Profit% | (Profit ÷ CP) × 100 |
| Loss% | (Loss ÷ CP) × 100 |
| SP (in case of profit) | CP × (100 + Profit%) ÷ 100 |
| SP (in case of loss) | CP × (100 − Loss%) ÷ 100 |
| CP (in case of profit) | SP × 100 ÷ (100 + Profit%) |
| CP (in case of loss) | SP × 100 ÷ (100 − Loss%) |
| Discount | MP − SP |
| Discount% | (Discount ÷ MP) × 100 |
Successive Profit/Loss Formula
When there are two successive profits (or losses) of x% and y%, the net percentage change is:
Net % Change = x + y + (xy ÷ 100)
This formula works for two successive profits, two successive losses (using negative values), or one profit and one loss (using the appropriate signs for each).
Useful Shortcut Conversions
| Percentage | Fraction |
|---|---|
| 10% | 1/10 |
| 12.5% | 1/8 |
| 20% | 1/5 |
| 25% | 1/4 |
Quick Multiplication Factors
| Scenario | Multiply CP by |
|---|---|
| Profit 10% | 1.10 |
| Profit 20% | 1.20 |
| Profit 25% | 1.25 |
| Loss 10% | 0.90 |
| Loss 20% | 0.80 |
How to Solve Profit and Loss Questions
Follow this step-by-step method during your exam.
Step 1: Read the Question Carefully
Identify what’s given and what you need to find — Cost Price, Selling Price, Profit or Loss percentage, Marked Price, or Discount percentage.
Step 2: Identify the Type of Question
Determine which formula category applies: basic profit/loss calculation, finding CP or SP, a discount problem, successive profit/loss, or overall profit/loss across multiple transactions.
Step 3: Write Down the Given Values
List every known value clearly — CP, SP, Profit%, Loss% — so nothing gets lost partway through the calculation.
Step 4: Select the Correct Formula
Choose the formula that matches what’s given and what’s being asked.
Step 5: Solve Step by Step
Work through the calculation carefully, especially when percentages are involved.
Step 6: Verify Your Answer
Check that the result makes logical sense: profit% should be positive when SP > CP, loss% should be positive when CP > SP, and SP should be above CP for a profit or below it for a loss.
Types of Profit and Loss Questions
Profit and loss problems generally fall into a handful of recurring patterns:
- Finding profit or loss percentage when CP and SP are given
- Finding selling price when the profit percentage is given
- Finding cost price when SP and profit percentage are given
- Discount problems involving marked price and discount percentage
- Two articles sold at the same price, one at a profit and one at a loss
- Successive profit or loss, applied one after another
- Overall profit when different portions of stock are sold at different rates
Finding Profit or Loss Percentage
Example: A man buys an article for $500 and sells it for $600. Find his profit percentage. Profit = SP − CP = 600 − 500 = 100, and expressing that as a percentage of CP gives Profit% = (100 ÷ 500) × 100. Answer: 20%
Finding Selling Price When Profit% is Given
Example: The cost price of an article is ₹866. If it is sold at a profit of 35%, what is the selling price? SP = CP × (100 + Profit%) ÷ 100 = 866 × 135 ÷ 100. Answer: ₹1169.10
Finding Cost Price When SP and Profit% are Given
Example: By selling a cap for Rs. 29.75, a man gains 6.25%. What was the CP of the cap? CP = SP × 100 ÷ (100 + Profit%) = 29.75 × 100 ÷ 106.25. Answer: ₹28
Discount Problems
Example: A trader marks his goods 20% above cost price and allows a 10% discount. What is his gain percentage? Taking CP as 100, the marked price becomes 120, the 10% discount on that is 12, so the selling price is 108 — an 8% gain over the original cost price. Answer: 8%
Two Articles Sold at the Same Price
Example: A man sells two items for ₹500 each, one at a 25% gain and the other at a 25% loss. What is the overall gain or loss? The item sold at a profit had a cost price of 500 × 100 ÷ 125 = 400, and the item sold at a loss had a cost price of 500 × 100 ÷ 75 ≈ 666.67. The combined cost price (1066.67) exceeds the combined selling price (1000), so the deal results in an overall loss. Answer: 6.25% loss
Successive Profit or Loss
Example: An item is sold at a 10% loss. If it had been sold for ₹40 more, there would have been a 10% profit. What is the cost price? If CP = x, the loss-sale price is 0.90x and the profit-sale price is 1.10x; the ₹40 gap between them equals 0.20x, so x = 40 ÷ 0.20. Answer: ₹200
Overall Profit Across Different Rates
Example: A merchant bought goods worth Rs. 6000 and sold half at a 12% profit. At what profit percent should he sell the other half to reach an overall profit of 18%? The first half (CP 3000) sold at 12% profit brings in 3360. To hit an overall 18% profit on the full 6000, the total selling price must reach 7080, so the second half needs to sell for 3720 — a profit of 720 on its CP of 3000. Answer: 24%
Important Tricks
Trick 1: Use the Fraction Method
Convert common percentages to fractions for faster mental calculation: 10% = 1/10, 12.5% = 1/8, 20% = 1/5, 25% = 1/4.
Trick 2: Use Multiplication Factors
Instead of calculating percentages separately, multiply CP directly — for example, a 20% profit means multiplying CP by 1.20, and a 20% loss means multiplying by 0.80.
Trick 3: Remember the Rule of Fractions
For a profit of x%, use the fraction 100/(100 + x); for a loss of x%, use 100/(100 − x).
Trick 4: For “No Profit, No Loss” with Two Articles
When two articles are sold at different profit/loss percentages with no overall gain or loss, the cost prices are in the ratio of the loss percentage to the profit percentage — if the first is at x% profit and the second at y% loss, then CP₁ : CP₂ = y : x.
Trick 5: Adjust Selling Price for a Different Profit Target
If an article is sold for a given SP at a% profit and you want b% profit instead, the new SP = Old SP × (100 + b) ÷ (100 + a).
Trick 6: Calculate 10% Quickly
To find 10% of any amount, just move the decimal point one place to the left.
Trick 7: Calculate 5% Quickly
Find 10% first using the trick above, then take half of it.
Trick 8: Use the Unitary Method
For problems involving multiple items, find the value of one unit first, then scale it up to the full quantity.
Common Mistakes to Avoid
- Calculating profit% on SP instead of CP — profit and loss percentages are always taken relative to the cost price
- Mixing up MP, SP, and CP — keep the three prices clearly labeled to avoid plugging the wrong value into a formula
- Forgetting to apply the successive discount/profit formula correctly — a straight addition of two percentages is usually wrong; use the net % change formula
- Ignoring the sign in mixed profit/loss problems — treat a loss as a negative percentage when combining it with a profit
- Skipping verification — always check that a “profit” answer has SP above CP, and a “loss” answer has CP above SP
Quick Solving Checklist
Before selecting your answer, use this checklist:
- Read the question carefully
- Identified CP, SP, Profit%, or Loss%
- Selected the correct formula
- Converted percentages to fractions where helpful
- Used multiplication factors for speed
- Performed the calculations carefully
- Verified the answer makes logical sense
- Avoided spending too much time on one question
Practice Questions
Conclusion
Mastering the Profit and Loss Test is essential for the Nepal Army Officer Cadet Entrance Examination. Success requires systematic application of formulas — not guesswork — across scenarios involving cost price, selling price, discounts, marked price, and multiple transactions.
Follow this disciplined approach:
Read → Identify → Apply Formula → Calculate → Verify → Answer
Regular practice enhances pattern recognition, speed, logic, and accuracy.
This resource is part of the Officer Cadet Entrance Exam Preparation series, focusing on IQ and Logical Reasoning for the Nepal Army Officer Cadet Entrance Exam. For structured lessons, comprehensive practice banks, and mock tests, explore the Profit and Loss Test course on the Pratima Academy LMS.