How to Solve Cost Price to Marked Price Ratio Problems
Solve cost price to marked price ratio problems with the MP/CP = (1+p/100)/(1-d/100) formula, a worked example and practice questions.
Expected Interview Answer
Marked price is set above cost price to leave room for a discount while still yielding a profit, so Selling Price = Marked Price × (1 - discount/100) = Cost Price × (1 + profit/100), and solving for the ratio Marked Price : Cost Price rearranges this equation.
The marking-up-then-discounting chain has three prices in play: Cost Price (CP), Marked Price (MP), and Selling Price (SP), linked by SP = MP × (1 - d/100) and SP = CP × (1 + p/100), where d is the discount percent and p is the desired profit percent. Setting these equal gives MP/CP = (1 + p/100) / (1 - d/100), the direct formula for the ratio. This shows that a seller must mark up by more than the intended profit margin, because part of the markup is “given back” through the discount. Always double-check by computing SP two ways from your final numbers to catch algebra slips.
- One equation (SP = MP×(1-d/100) = CP×(1+p/100)) covers markup, discount and profit together
- The ratio formula MP/CP = (1+p/100)/(1-d/100) solves most variants directly
- Cross-checking SP both ways catches setup errors quickly
AI Mentor Explanation
A team's target run rate is set higher than the rate they actually need, because rain delays or wickets falling might force a revised, lower “discounted” chase rate later. If they need to average 6 runs per over after the discount but marked their initial pace at a higher rate to buffer for setbacks, the ratio of marked pace to needed pace tells you how much cushion was built in. Cost-to-marked-price ratio problems work the same way: the marked figure is deliberately inflated above the target so a later reduction still lands on the required outcome.
Worked example (find MP:CP ratio)
Target profit
- 1 + 20/100 = 1.20
Planned discount
- 1 - 10/100 = 0.90
Ratio MP:CP
- 1.20/0.90 = 4:3
Step-by-Step Explanation
Step 1
Write both SP expressions
SP = MP × (1 - d/100) and SP = CP × (1 + p/100).
Step 2
Set them equal
MP × (1 - d/100) = CP × (1 + p/100).
Step 3
Solve for the ratio
MP/CP = (1 + p/100) / (1 - d/100).
Step 4
Verify with actual numbers
Plug back in and confirm SP matches from both formulas.
What Interviewer Expects
- Correct identification of CP, MP and SP roles in the equation
- Accurate derivation of MP/CP = (1+p/100)/(1-d/100)
- Understanding why MP must exceed CP by more than just the target profit
- Verification of the answer by recomputing SP both ways
Common Mistakes
- Confusing discount percentage (on MP) with profit percentage (on CP)
- Applying the discount to the cost price instead of the marked price
- Forgetting that MP must overshoot the target profit margin to absorb the discount
- Algebra errors when isolating the MP/CP ratio
Best Answer (HR Friendly)
“There are three prices to track — cost, marked, and selling — and the selling price is the bridge between them: it equals the marked price after the discount, and it also equals the cost price plus the intended profit. Setting those two expressions for selling price equal and solving gives the ratio of marked price to cost price directly, as one plus the profit fraction divided by one minus the discount fraction. The key insight is that the markup always has to be bigger than the profit margin alone, because part of it gets eaten by the discount.”
Follow-up Questions
- How would you find the discount percentage if MP, CP and desired profit are known?
- What happens to the MP:CP ratio if the discount is doubled but profit target stays fixed?
- How would you solve this if two successive discounts are offered on the marked price?
- How do you find the marked price directly when only cost price, profit percent, and discount percent are given?
MCQ Practice
1. A shopkeeper wants 25% profit after offering a 20% discount on the marked price. What is MP:CP?
MP/CP = 1.25/0.80 = 125/80 = 25/16, so MP:CP = 25:16.
2. Cost price is 600. Marked price is 900. A discount is given so the seller earns exactly 20% profit. The discount percentage is?
SP needed = 600 × 1.20 = 720. Discount = 900 - 720 = 180, and 180/900 = 20%.
3. If MP:CP = 3:2 and the discount offered is 10%, the profit percentage is?
Let CP = 2, MP = 3. SP = 3 × 0.90 = 2.70. Profit % = (2.70-2)/2 × 100 = 35%.
Flash Cards
Equation linking CP, MP, SP? — SP = MP × (1 - d/100) = CP × (1 + p/100).
Formula for MP:CP ratio? — MP/CP = (1 + p/100) / (1 - d/100).
Why must MP exceed the target profit margin? — Because the discount eats into the markup before profit is realized.
How to verify an MP:CP answer? — Recompute SP from both the MP-discount route and the CP-profit route; they must match.