NIFT GAT Previous Year Questions: Mastering Successive Discounts and Retail Math
For any aspiring fashion technologist or designer appearing for the National Institute of Fashion Technology Entrance Exam, the General Ability Test (GAT) serves as a critical bridge to success. Among the various quantitative sections, Retail Inventory Mathematics—specifically the calculation of successive discounts and mark-up percentages—stands out as a perennial favorite for examiners. Why? Because these concepts directly mirror the real-world financial logic of the fashion industry. Whether you are managing a boutique or a high-street brand, understanding how price fluctuations impact margins is essential.
In this comprehensive decoder, we analyze patterns from several Previous Year Questions to help you move beyond traditional, time-consuming methods. We will explore the ‘Ninja Shortcuts’ that allow you to solve complex percentage problems in under 30 seconds, ensuring you have more time to tackle the analytical and linguistic sections of the GAT.
Core Concepts: The Retailer’s Pricing Ladder
Before diving into the questions, let us establish the vocabulary of retail math. There are three pillars you must master:
- Cost Price (CP): The price at which the retailer buys the product.
- Marked Price (MP) or List Price: The price displayed on the tag, usually higher than CP to allow for discounts.
- Selling Price (SP): The final price at which the product is sold after all discounts are applied.
The Mark-up Percentage is always calculated on the Cost Price, while the Discount Percentage is always calculated on the Marked Price. This distinction is the most common trap in Previous Year Questions.
💡 Why do retailers use Successive Discounts?
Retailers use successive discounts (e.g., 20% + 10% off) because it sounds more attractive than a single 28% discount, even though the net reduction is exactly the same. Psychologically, customers see ‘two discounts’ and perceive a higher value, even if the math says otherwise.
Question 1: The Classic Double Discount Dilemma
Problem: A luxury leather handbag is marked at 8,000 INR. The store offers a festive discount of 20% followed by an additional seasonal clearance discount of 10%. What is the final selling price of the handbag?
The Traditional Method (The Slow Way)
Step 1: Calculate the first discount: 20% of 8,000 = (20/100) * 8,000 = 1,600 INR.
Step 2: New Price after first discount = 8,000 – 1,600 = 6,400 INR.
Step 3: Calculate the second discount on the new price: 10% of 6,400 = (10/100) * 6,400 = 640 INR.
Step 4: Final Selling Price = 6,400 – 640 = 5,760 INR.
The 30-Second Ninja Shortcut
Use the Effective Discount Formula: x + y – (xy/100)
Here, x = 20 and y = 10.
Effective Discount = 20 + 10 – (20 * 10 / 100) = 30 – 2 = 28%.
If the discount is 28%, the Selling Price is (100 – 28) = 72% of the Marked Price.
72% of 8,000 = 0.72 * 8,000 = 5,760 INR.
Question 2: Finding the Mark-up Percentage
Problem: A fashion retailer buys a silk scarf for 1,200 INR. They want to offer a 20% discount to customers and still make a 20% profit on the cost price. At what price should they mark the product?
The Traditional Method
Target Profit = 20% of 1,200 = 240 INR.
Target Selling Price (SP) = 1,200 + 240 = 1,440 INR.
Now, we know SP = MP * (100 – Discount%)/100.
1,440 = MP * (80/100).
MP = (1,440 * 100) / 80 = 1,800 INR.
The 30-Second Ninja Shortcut
Use the MP/CP Ratio Formula: MP/CP = (100 + Profit%) / (100 – Discount%)
MP / 1,200 = (100 + 20) / (100 – 20)
MP / 1,200 = 120 / 80
MP / 1,200 = 3 / 2
MP = 1,200 * 1.5 = 1,800 INR.
Question 3: Triple Successive Discounts
Problem: Based on patterns seen in several Previous Year Questions, finding the single equivalent discount for three successive rates is a common challenge. Find the single equivalent discount for 20%, 15%, and 10%.
The Traditional Method
Assume Marked Price is 100.
After 20% off: 80.
After 15% off: 80 – (0.15 * 80) = 80 – 12 = 68.
After 10% off: 68 – (0.1 * 68) = 68 – 6.8 = 61.2.
Single Equivalent Discount = 100 – 61.2 = 38.8%
The 30-Second Ninja Shortcut
Use Multipliers! A discount of 20% means you pay 0.8. A discount of 15% means you pay 0.85. A discount of 10% means you pay 0.9.
Final Price Ratio = 0.8 * 0.85 * 0.9 = 0.612.
Discount = 1 – 0.612 = 0.388 or 38.8%
Question 4: Reverse Engineering the Cost Price
Problem: After allowing a discount of 12% on the marked price of a garment, a shopkeeper still makes a profit of 32%. If the marked price is 1,500 INR, what was the cost price?
The Traditional Method
Step 1: Find Selling Price. SP = 1,500 * (100-12)/100 = 1,500 * 0.88 = 1,320 INR.
Step 2: We know SP = CP * (100 + Profit%)/100.
1,320 = CP * (132/100).
CP = (1,320 * 100) / 132 = 1,000 INR.
The 30-Second Ninja Shortcut
Using the Ratio Method again: CP/MP = (100 – Discount%) / (100 + Profit%)
CP / 1,500 = (100 – 12) / (100 + 32)
CP / 1,500 = 88 / 132 = 2 / 3 (Dividing both by 44)
CP = (2/3) * 1,500 = 1,000 INR.
Question 5: Advanced Inventory Mark-up Logic
Problem: A merchandiser marks their inventory 50% above the cost price. They sell half the stock at the marked price, one-fourth at a 20% discount, and the remaining at a 40% discount. What is the overall profit percentage?
The Traditional Method
Let Total Items = 100, CP of each = 1. Total CP = 100. MP of each = 1.5.
Group 1 (50 items): SP = 50 * 1.5 = 75.
Group 2 (25 items): SP = 25 * (1.5 * 0.8) = 25 * 1.2 = 30.
Group 3 (25 items): SP = 25 * (1.5 * 0.6) = 25 * 0.9 = 22.5.
Total SP = 75 + 30 + 22.5 = 127.5.
Profit = 127.5 – 100 = 27.5%
💡 Click to Reveal the Inventory Shortcut
Always assume the Total CP is 100 for percentage-based inventory problems. If the question gives you fractions like half (1/2) and one-fourth (1/4), use a total quantity that is easily divisible by 4. This avoids decimals early in the calculation!
Cheat Sheet: Quick Revision Formulas
| Scenario | Formula |
|---|---|
| Two Successive Discounts | x + y – (xy/100) |
| Relationship between MP, CP, P%, D% | MP/CP = (100 + P%) / (100 – D%) |
| Net Change (Mark-up & Discount) | Mark-up% – Discount% – (M%*D%/100) |
| Selling Price from MP | SP = MP * (1 – D1/100) * (1 – D2/100)… |
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