How to Solve Profit and Loss Problems
Solve profit and loss aptitude problems — cost price base, profit and loss formulas, marked price and discounts — with a worked example and practice questions.
Expected Interview Answer
Profit and loss are always calculated on the cost price: Profit = SP − CP, Loss = CP − SP, and the percentage is (Profit or Loss ÷ CP) × 100.
Cost price (CP) is what you pay, selling price (SP) is what you sell for. Profit% and Loss% are measured against CP, not SP — the most common error. Useful relations: SP = CP × (1 + profit%/100), and CP = SP ÷ (1 + profit%/100). For discount problems, discount is on the marked price, while profit is still on the cost price, so keep the two bases separate.
- One base (cost price) anchors every calculation
- Simple formulas cover most variations
- Extends to discount, marked-price and markup problems
AI Mentor Explanation
Think of a franchise buying a player for a fee (cost price) and later selling the contract (selling price). Whether they profited is judged against what they paid, not what they sold for — that base is the cost price. A player bought cheap and sold high shows profit measured on the buy price. Profit-and-loss works exactly so: profit or loss is always a percentage of the cost price, never the selling price.
Worked example
Cost Price
- CP = 200
Selling Price
- SP = 250
Profit
- SP − CP = 50
- 50 ÷ 200 × 100 = 25%
Step-by-Step Explanation
Step 1
Identify CP and SP
Cost price is what you paid; selling price is what you sold for.
Step 2
Compute profit or loss
Profit = SP − CP (positive) or Loss = CP − SP.
Step 3
Percentage on CP
(Profit or Loss ÷ CP) × 100 — always divide by cost price.
Step 4
Discounts separately
Discount is on the marked price; profit is still on the cost price.
What Interviewer Expects
- Profit/loss percentage measured on cost price
- The SP = CP(1 + profit%/100) relation
- Separating discount (marked price) from profit (cost price)
- Finding CP from SP and profit%
Common Mistakes
- Calculating profit% on the selling price
- Confusing marked price with cost price
- Applying discount to the cost price
- Sign errors between profit and loss
Best Answer (HR Friendly)
“Profit and loss are always figured on the cost price — what you paid. Profit is selling price minus cost price, and the percentage is that gain divided by the cost price times 100. The classic mistake is dividing by the selling price instead.”
Code Example
def profit_percent(cp, sp):
return (sp - cp) / cp * 100
print(profit_percent(200, 250)) # 25.0 (%)
# Selling price from cost and desired profit%
def selling_price(cp, profit_pct):
return cp * (1 + profit_pct / 100)
print(selling_price(200, 25)) # 250.0Follow-up Questions
- How do you find the cost price given selling price and profit%?
- What is the difference between marked price and selling price?
- How do successive discounts combine?
- If two items sell at the same price, one at 20% profit and one at 20% loss, is there net profit or loss?
MCQ Practice
1. CP = 400, SP = 500. Profit% is?
Profit = 100; 100 ÷ 400 × 100 = 25%.
2. Profit percentage is always calculated on the?
By convention, profit and loss percentages use the cost price as the base.
3. Discount is applied to the?
Discount reduces the marked (list) price to reach the selling price.
Flash Cards
Profit formula? — Profit = SP − CP; Profit% = (Profit ÷ CP) × 100.
What is the base for profit%? — The cost price — never the selling price.
SP from CP and profit%? — SP = CP × (1 + profit%/100).
Discount base? — The marked price, not the cost price.