Profit and Loss Test: IQ and Logical Reasoning Questions, Tricks, and Practice

Profit and Loss Test is an important part of IQ and Logical Reasoning that tests your ability to calculate profit, loss, discounts, and marked prices in different business transactions.

For Officer Cadet Entrance Exam preparation, these questions help develop numerical ability, arithmetic skills, logical thinking, and accuracy in applying profit and loss formulas. Explore the complete Officer Cadet Exam resources and IQ for Officer Cadet preparation for additional practice and study materials.

What is Profit and Loss Test?

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 Rs. 500 and sells it for Rs. 600. Find his profit percentage.
Solution:
The profit is the difference between selling price and cost price, and expressing that as a share of the cost price gives the percentage.
Profit = Selling Price – Cost Price
Profit = 600 – 500 = Rs. 100
Profit Percentage = $\frac{Profit}{Cost Price}\times 100$

Profit Percentage = $\frac{100}{500} \times 100$
Profit Percentage = 0.2 x 100
Profit Percentage = 20%
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 Profit and Loss Test 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

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).

Types of Profit and Loss Test Questions

Profit and loss problems generally fall into a handful of recurring patterns:

1. Finding Profit or Loss Percentage

Finding profit or loss percentage when CP and SP are given
Example:
A man buys an article for $800 and sells it for $600. Find his loss percentage.
Solution:
Loss = CP − SP = 800 − 600 = 200
Loss% = (Loss ÷ CP) × 100 = (200 ÷ 800) × 100 = 25%
Answer: 25%

2. Finding Selling Price When Profit% is Given

Finding selling price when the profit percentage is given.
Example:
The cost price of an article is Rs 1200. If it is sold at a profit of 25%, what is the selling price?
Solution:
SP = CP × (100 + Profit%) ÷ 100
SP = 1200 × (100 + 25) ÷ 100
SP = 1200 × 125 ÷ 100
SP = 150000 ÷ 100
SP = Rs 1500
Answer: Rs 1500

3. Finding Cost Price When SP and Profit% are Given

Finding cost price when SP and profit percentage are given.
Example:
By selling a bag for Rs. 450, a man gains 12.5%. What was the CP of the bag?
Solution:
CP = SP × 100 ÷ (100 + Profit%)
CP = 450 × 100 ÷ (100 + 12.5)
CP = 450 × 100 ÷ 112.5
CP = 45000 ÷ 112.5
CP = Rs 400
Answer: Rs 400

4. Discount Problems

Discount problems involving marked price and discount percentage.
Example:
A trader marks his goods 40% above cost price and allows a 25% discount. What is his gain percentage?
Solution:
Let CP = 100
Marked Price = 100 + 40% of 100 = 140
Discount = 25% of 140 = 35
Selling Price = 140 − 35 = 105
Gain = SP − CP = 105 − 100 = 5
Gain% = (Gain ÷ CP) × 100 = (5 ÷ 100) × 100 = 5%
Answer: 5%

5. Two Articles Sold at the Same Price

Two articles sold at the same price, one at a profit and one at a loss.
Example:
A man sells two items for ₹600 each, one at a 20% gain and the other at a 20% loss. What is the overall gain or loss?
Solution:
Item sold at 20% profit:
CP₁ = SP × 100 ÷ (100 + Profit%) = 600 × 100 ÷ 120 = ₹500
Item sold at 20% loss:
CP₂ = SP × 100 ÷ (100 − Loss%) = 600 × 100 ÷ 80 = ₹750
Combined CP = 500 + 750 = ₹1250
Combined SP = 600 + 600 = ₹1200
Loss = CP − SP = 1250 − 1200 = ₹50
Loss% = (Loss ÷ CP) × 100 = (50 ÷ 1250) × 100 = 4%
Answer: 4% loss
Shortcut: When two articles are sold at the same price, one at x% profit and the other at x% loss, the overall result is always a loss of (x ÷ 10)² % = (20 ÷ 10)² = 4% loss.

6. Successive Profit or Loss

Successive profit or loss, applied one after another.
Example:
An item is sold at a 20% loss. If it had been sold for Rs 120 more, there would have been a 20% profit. What is the cost price?
Solution:
Let CP = x
Selling price at 20% loss = 0.80x
Selling price at 20% profit = 1.20x
Difference between the two selling prices = 1.20x − 0.80x = 0.40x
Given, difference = Rs 120
So, 0.40x = 120
x = 120 ÷ 0.40
x = Rs 300
Answer: Rs 300

7. Overall Profit Across Different Rates

Overall profit when different portions of stock are sold at different rates.
Example:
A merchant bought goods worth Rs. 8000 and sold half at a 15% profit. At what profit percent should he sell the other half to reach an overall profit of 20%?
Solution:
Total CP = Rs 8000
Overall profit target = 20%
Total SP required = 8000 × (100 + 20) ÷ 100 = 8000 × 120 ÷ 100 = Rs 9600
First half CP = 8000 ÷ 2 = Rs 4000
First half sold at 15% profit:
SP₁ = 4000 × (100 + 15) ÷ 100 = 4000 × 115 ÷ 100 = Rs 4600
Second half CP = Rs 4000
SP₂ required = Total SP − SP₁ = 9600 − 4600 = Rs 5000
Profit on second half = SP₂ − CP₂ = 5000 − 4000 = Rs 1000
Profit% on second half = (Profit ÷ CP) × 100 = (1000 ÷ 4000) × 100 = 25%
Answer: 25%

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.

Effective Tricks to Solve Profit and Loss Questions

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.

Important Tips to Solve Profit and Loss Questions

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.

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