How to Solve Discount and Marked Price Problems
Solve discount and marked price aptitude problems, including successive discounts and equivalent single discount, with worked examples and MCQs.
Expected Interview Answer
Selling price equals marked price minus discount, SP = MP x (1 - discount%/100), and successive discounts must be chained as multiplying factors rather than added together.
The marked price is the labeled or listed price before any reduction; the discount is a percentage taken off that marked price to reach the selling price. When a shop offers two discounts back to back, such as 10% and then 20%, the combined effect is SP = MP x 0.90 x 0.80, not a flat 30% off, because the second discount applies to the already-reduced price. This mirrors successive percentage change: use the shortcut a + b + ab/100 with negative signs to find the single equivalent discount. A common trap question also involves marking up the price above cost first, then discounting it, so the final selling price can still exceed the original cost even after an apparently large discount.
- SP = MP x (1 - d/100) anchors every discount problem
- Successive discounts chain as factors, never as a simple sum
- Exposes the mark-up-then-discount trick used in trap questions
AI Mentor Explanation
A cricket bat’s marked price is 4000, discounted 25% for a season sale, giving a selling price of 4000 x 0.75 = 3000. If the shop then applies a further 10% loyalty discount, it is 3000 x 0.90 = 2700, not a flat 35% off 4000, which would wrongly give 2600. Marked-price problems always chain successive discounts as multiplying factors on the reduced price, exactly like successive percentage change.
Worked example (successive discounts)
After 10% discount
- 4000 x 0.90 = 3600
After 20% more
- 3600 x 0.80 = 2880
Equivalent single discount
- 10+20+2 = 28%
Step-by-Step Explanation
Step 1
Identify marked price and discount %
SP = MP x (1 - discount/100) for a single discount.
Step 2
Chain successive discounts as factors
Apply each discount to the previous result, never to the original marked price.
Step 3
Use the equivalent single discount shortcut
For two discounts a% and b%: equivalent discount = a + b - ab/100.
Step 4
Watch for mark-up-then-discount traps
A price marked up above cost, then discounted, can still leave a profit — check against the original cost.
What Interviewer Expects
- Correct SP = MP x (1 - discount/100) relationship
- Chaining successive discounts multiplicatively rather than adding percentages
- Deriving the equivalent single discount for two successive discounts
- Spotting mark-up-then-discount trap scenarios relative to cost price
Common Mistakes
- Adding two discount percentages directly instead of chaining the factors
- Applying both discounts to the original marked price instead of sequentially
- Confusing discount percentage (on marked price) with profit percentage (on cost price)
- Forgetting that marking up then discounting can still yield a profit over cost
Best Answer (HR Friendly)
“Selling price is always marked price times one minus the discount fraction, and when there are two discounts, I apply them one after another to the running price rather than adding the percentages. For example, 10% then 20% off is not 30% off — it works out to a 28% equivalent single discount, because the second cut applies to an already-reduced amount.”
Follow-up Questions
- How do you find the marked price if the selling price and discount percentage are known?
- How does discount percentage differ from profit percentage when cost price is involved?
- How would you find the single equivalent discount for three successive discounts?
- Why might a shop mark up a price by 40% and still offer a "40% off" sale without a loss?
MCQ Practice
1. A shirt is marked at 1200 and sold after a 15% discount. The selling price is?
SP = 1200 x (1 - 15/100) = 1200 x 0.85 = 1020.
2. Successive discounts of 10% and 10% are equivalent to a single discount of?
Equivalent discount = 10 + 10 - (10)(10)/100 = 20 - 1 = 19%.
3. A marked price is 5000. After a discount, the selling price is 4250. The discount percentage is?
Discount = (5000 - 4250)/5000 x 100 = 750/5000 x 100 = 15%.
Flash Cards
Selling price formula from marked price? — SP = MP x (1 - discount%/100).
Equivalent single discount for a% and b%? — a + b - ab/100.
Do successive discounts apply to the original price? — No — each discount applies to the price after the previous discount.
Marked-up-then-discounted trap? — A price marked up above cost and then discounted can still be sold at a profit over cost.