Discount Mastery: Scenario Bank
Exam-Oriented Case Studies for Advanced Aptitude Preparation
1. Concept
In competitive exams, Discount is rarely a direct calculation. It is usually part of a multi-step scenario involving supply chains, inventory clearance, or tax implications. Success depends on identifying the base (Marked Price) and applying percentage changes sequentially.
2. Important Formulas
• Profit/Markup Bridge: $\frac{MP}{CP} = \frac{100 + \text{Gain}\%}{100 - \text{Discount}\%}$
• Free Inventory Rule: Discount % = $\frac{\text{Free Quantity}}{\text{Total Shipped Quantity}} \times 100$
Q1. A retail giant marks an Ultra-HD TV at $120,000. During a clearance event, they offer a 15% trade-in discount. A customer further applies a 5% loyalty coupon on the reduced price. What is the final transaction value?
Step 2: 5% discount on 102,000 = 102,000 - 5,100 = $96,900.
Q2. A wholesaler provides two successive discounts of 20% and 10% to a retailer. If the retailer wants to switch to a single flat discount that results in the same price, what should the percentage be?
$20 + 10 - \frac{200}{100} = 30 - 2 = 28\%$.
Q3. A lifestyle brand runs a promotion: "Buy 7 luxury shirts and walk away with 3 additional shirts for free." A competitor claims this is a 40% discount. Is the competitor correct? What is the actual discount?
Free shirts = 3.
Discount % = $\frac{3}{10} \times 100 = 30\%$.
Q4. A jeweler marks their inventory such that even after offering a 25% discount to customers, they secure a net profit of 20% on the cost price. By what percentage was the item marked up initially?
A ratio of 1.6 represents a 60% markup.
Q5. A distributor receives an invoice of $12,750 for a batch of machinery after a flat 15% seasonal discount. What was the original list price displayed in the catalog?
$12750 = 0.85 \times MP$.
$MP = \frac{12750}{0.85} = 15,000$.
Q6. An importer offers a "10-20-30" discount scheme (10%, then 20%, then 30% successively) for bulk orders. A buyer mistakenly thinks this adds up to a 60% discount. What is the real effective discount?
Effective Discount $= (1 - 0.504) \times 100 = 49.6\%$.
Q7. A premium watch with an MP of $2,000 is sold for $1,530 after two successive discounts. If the first discount is known to be 10%, what is the percentage of the second discount?
Step 2: Second Discount Amount $= 1,800 - 1,530 = 270$.
Rate: $\frac{270}{1,800} \times 100 = 15\%$.
Q8. A shopkeeper aggressive marks his goods 50% above the cost price. To attract customers, he then offers a 50% discount. What is the net financial impact on his business per item?
$\frac{50^2}{100} = 25\%$ Loss.
Q9. A distributor buys an appliance for $2,700. They want to earn a 20% profit while also offering customers a 10% cash-payment discount. What must be the sticker price (MP)?
$MP = 2700 \times \frac{120}{90} = 2700 \times \frac{4}{3} = 3,600$.
Q10. A firm is debating between two marketing campaigns: Campaign X offers a single 45% discount. Campaign Y offers three successive discounts of 20%, 20%, and 5%. Which is better for the consumer?
Campaign Y: $SP = 0.8 \times 0.8 \times 0.95 = 0.608$. Discount $= 39.2\%$.
X is significantly better for the consumer.
Q11. A trader buys a consignment at a 30% discount on the MP. He then sells it at a 5% discount on the same MP. What is his actual profit percentage on his investment?
Profit $= 25$.
Profit % $= \frac{25}{70} \times 100 = 35.71\%$.
Q12. A smartphone is marked at $50,000. The store offers a 10% discount, but the government mandates a 12% Sales Tax on the final transaction price. What is the net cost to the buyer?
Tax: $12\%$ of $45,000 = 5,400$.
Total: $45,000 + 5,400 = $50,400.
Q13. A product was marked up by 80% over the cost price. After two equal successive discounts of $x\%$, the product is sold exactly at its cost price. What is the value of $x$?
Total Discount multiplier needed $= \frac{100}{180} = 0.555$.
$(1 - \frac{x}{100})^2 = 0.555 \Rightarrow (1 - \frac{x}{100}) = 0.745$.
$x \approx 25.46\%$.
Q14. A manufacturer offers three sets of discounts: (A) 25% and 15%, (B) 30% and 10%, (C) 35% and 5%. If you are the seller, which scheme results in the highest selling price (lowest loss for you)?
Q15. If a retailer marks the price of an item 5 times the cost price, and then offers a generous "Half-Price" discount, what is the profit percentage realized?
Half-price Discount ($50\%$) means $SP = 250$.
Profit $= 150$ on $100 = 150\%$.
Q16. In a financial report, the ratio of the net selling price to the listed marked price is found to be 13:20. What is the percentage of discount offered during that period?
Discount % $= \frac{7}{20} \times 100 = 35\%$.
Q17. A retailer allows a 10% cash discount and also gives 1 free item for every 9 items purchased. He still manages to gain 20% profit. By what percentage was the markup set initially?
Successive Discounts of $10\%$ and $10\% = 19\%$.
Ratio: $\frac{MP}{CP} = \frac{100+20}{100-19} = \frac{120}{81} \approx 1.48$ (actually closer to $50\%$ considering specific unit math).
Q18. On a purchase of $10,000, a buyer is offered a choice between a direct 45% discount or three successive discounts of 30%, 10%, and 5%. What is the difference in dollars between the two options?
Option B: $SP = 10,000 \times 0.7 \times 0.9 \times 0.95 = 5,985$.
Difference: $5,985 - 5,500 = $485. (Corrected calculation for clarity: 515 is correct if Option A is better).
Q19. A stockist marks an item at $40,000. He offers a 15% discount but charges a 5% commission on the Selling Price from the buyer. What is the net amount received by the stockist?
Commission added to receipt $= 34,000 \times 1.05 = $35,700.
Q20. A luxury showroom is forced to clear inventory at a 40% discount. To ensure they at least break even (zero profit/loss), what was the minimum required markup they should have applied to the Cost Price?
We know $SP = 0.6 \times MP$.
Therefore, $CP = 0.6 \times MP \Rightarrow MP = \frac{1}{0.6} CP = 1.6667 CP$.
Markup $= 66.67\%$.