Profit Percentage on Cost Price vs Selling Price
Understand why profit percentage differs on cost price vs selling price, with formulas, a worked example and practice questions.
Expected Interview Answer
Profit percentage is almost always calculated on cost price by default (Profit% = (SP - CP)/CP x 100), but the same absolute profit expressed as a percentage of selling price gives a different, smaller number, and conflating the two is the single most common error in profit-and-loss problems.
If cost price is 100 and selling price is 120, the profit of 20 is 20% of cost price but only about 16.67% of selling price — the denominator changes the answer even though the numerator (the absolute profit) stays fixed. Unless a problem explicitly says 'profit on selling price,' assume cost price is the base, since that is the standard convention in aptitude tests and real accounting. The two are related by Profit%(on SP) = Profit%(on CP) / (1 + Profit%(on CP)/100), a conversion worth memorizing for problems that mix the two bases. Always state which base you are using when reporting a profit percentage, because the same deal can be legitimately described two different ways.
- Prevents the most common profit-and-loss calculation error
- Cost-price-as-default convention resolves ambiguous wording
- One conversion formula bridges CP-based and SP-based percentages
- Forces explicit labeling, avoiding miscommunication in real pricing
AI Mentor Explanation
A bowler concedes 20 extra runs above a baseline economy target of 100 runs — expressed against the baseline (like cost price) that’s a 20% overrun, but expressed against the actual runs conceded, 120 (like selling price), it’s only about 16.67%. The same 20-run gap reads as two different percentages depending on which total you divide by, exactly like profit percentage on cost versus on selling price.
Worked example
Given
- CP = 100, SP = 120
- Profit = 20
On cost price
- 20/100 x 100 = 20%
On selling price
- 20/120 x 100 = 16.67%
Step-by-Step Explanation
Step 1
Compute absolute profit
Profit = SP - CP, fixed regardless of the base chosen.
Step 2
Default to cost price
Profit% = (SP - CP)/CP x 100 unless the question says otherwise.
Step 3
Compute on selling price if asked
Profit% = (SP - CP)/SP x 100 — always the smaller number.
Step 4
Convert between bases if needed
Profit%(SP) = Profit%(CP) / (1 + Profit%(CP)/100).
What Interviewer Expects
- Correct default to cost price as the base
- Ability to compute profit% on selling price when explicitly asked
- Understanding why profit%(SP) is always smaller than profit%(CP) for the same deal
- Correct use of the CP-to-SP percentage conversion formula
Common Mistakes
- Assuming both bases give the same percentage
- Using selling price as the base without the question specifying it
- Sign errors when profit is actually a loss (loss% also defaults to cost price)
- Misapplying the conversion formula direction (CP-based to SP-based vs the reverse)
Best Answer (HR Friendly)
“Profit percentage is calculated on cost price by default — profit divided by cost price, times 100 — unless the question explicitly asks for it on selling price, in which case you divide by the selling price instead, which always gives a smaller number for the same deal. I always check which base the question wants before computing, because the same absolute profit legitimately reports as two different percentages depending on the denominator.”
Follow-up Questions
- How do you convert a profit percentage on selling price back to one on cost price?
- How does this same cost-vs-sale base distinction apply to loss percentage?
- Why do businesses sometimes prefer quoting margin on revenue (selling price) instead of cost?
- How would you solve for cost price given only the selling price and a profit percentage on selling price?
MCQ Practice
1. CP = 200, SP = 250. Profit percentage on cost price is?
Profit = 50. 50/200 x 100 = 25%.
2. CP = 200, SP = 250. Profit percentage on selling price is?
Profit = 50. 50/250 x 100 = 20%.
3. If profit is 25% on cost price, the profit percentage on selling price is?
25 / (1 + 25/100) = 25/1.25 = 20%.
Flash Cards
Default base for profit percentage? — Cost price, unless the question specifies selling price.
Formula for profit% on CP? — (SP - CP)/CP x 100.
Formula for profit% on SP? — (SP - CP)/SP x 100 — always smaller than profit% on CP.
Conversion from CP-based to SP-based %? — Profit%(SP) = Profit%(CP) / (1 + Profit%(CP)/100).