NIFT GAT Previous Year Questions Decoder: Mastering Simple vs. Compound Interest with Fractional Rates

Introduction: Why Quantitative Ability is Your Secret Weapon for NIFT GAT

When you dream of walking the hallways of the National Institute of Fashion Technology, your mind is likely filled with sketches, textiles, and color palettes. However, the gatekeeper to those design studios is the General Ability Test (GAT). Among the various sections, Quantitative Ability often intimidates creative minds the most. Specifically, the comparison between Simple Interest and Compound Interest over a two-year period using fractional interest rates is a recurring theme in Previous Year Questions.

Understanding how money grows over time is not just a mathematical exercise; it is a business essential for future designers and fashion managers. Whether you are calculating the return on investment for a new boutique or understanding loan terms for a startup, these concepts are vital. In this guide, we will decode the complexity of fractional rates (like 12.5%, 16 2/3%, etc.) and provide you with shortcuts that turn a five-minute calculation into a thirty-second breeze.

The Foundation: Fractional Interest Rates Decoded

In many Previous Year Questions, the rate of interest is not a clean number like 10% or 20%. Instead, examiners use fractions like 12.5%, 14 2/7%, or 16 2/3%. Why? Because these numbers are designed to test if you can convert percentages to fractions to simplify your work.

• 12.5% = 1/8
• 16 2/3% = 1/6
• 14 2/7% = 1/7
• 11 1/9% = 1/9
• 9 1/11% = 1/11
• 6 1/4% = 1/16

By using the fraction instead of the percentage, you eliminate the decimal point nightmare. If the rate is 1/x, the difference between Compound Interest and Simple Interest for 2 years is always simply 1 unit if the Principal is assumed to be x-squared (x²).

Question 1: The Classic Difference Calculation

Question: Find the difference between the Compound Interest and Simple Interest on a sum of ₹12,800 for 2 years at 12.5% per annum.

The Traditional Method:

Step 1: Calculate SI = (P × R × T) / 100 = (12800 × 12.5 × 2) / 100 = 128 × 25 = ₹3,200.
Step 2: Calculate CI Amount = P(1 + R/100)² = 12800(1 + 12.5/100)² = 12800(1 + 1/8)² = 12800(9/8)² = 12800 × (81/64) = 200 × 81 = ₹16,200.
Step 3: CI = Amount – Principal = 16200 – 12800 = ₹3,400.
Step 4: Difference = CI – SI = 3400 – 3200 = ₹200.

The 30-Second Ninja Shortcut:

Identify the fraction: 12.5% = 1/8. Here, x = 8.
The formula for the difference for 2 years when R = 1/x is: Difference = Principal / x².
Difference = 12,800 / (8²) = 12,800 / 64 = ₹200.
Done! You just saved 3 minutes of complex multiplication.

Question 2: Finding the Principal from the Difference

Question: The difference between Simple Interest and Compound Interest for 2 years at 16 2/3% per annum is ₹50. Find the sum of money invested.

The Traditional Method:

Let the Principal be P. Difference = P(R/100)².
50 = P ( (50/3) / 100 )²
50 = P (1/6)²
50 = P/36
P = 50 × 36 = ₹1,800.

The 30-Second Ninja Shortcut:

Rate = 16 2/3% = 1/6. Let the Principal be x² (where x = 6).
So, let Principal = 36 units.
Interest for Year 1 (SI/CI) = 36 * 1/6 = 6 units.
Interest for Year 2 (SI) = 6 units.
Interest for Year 2 (CI) = 6 units + Interest on Year 1 interest = 6 + (6 * 1/6) = 7 units.
Total SI = 6 + 6 = 12 units. Total CI = 6 + 7 = 13 units.
Difference = 13 – 12 = 1 unit.
If 1 unit = ₹50, then 36 units (Principal) = 36 × 50 = ₹1,800.

Question 3: Working with 14 2/7% Fractional Rates

Question: If the Compound Interest on a certain sum for 2 years at 14 2/7% per annum is ₹450, find the Simple Interest on the same sum at the same rate for the same period.

The Traditional Method:

Rate = 14 2/7% = 1/7.
CI = P[(1 + 1/7)² – 1] = P[(8/7)² – 1] = P[64/49 – 1] = P(15/49).
Given CI = 450. So, 450 = P(15/49) -> P = (450 × 49) / 15 = 30 × 49 = ₹1,470.
Now, SI = (1470 × 1/7 × 2) = 210 × 2 = ₹420.

The 30-Second Ninja Shortcut:

Rate = 1/7. Assume Principal = 7² = 49 units.
Year 1 interest = 7 units. Year 2 SI = 7 units. Year 2 CI interest on interest = 7 * 1/7 = 1 unit.
Total CI = 7 + 7 + 1 = 15 units.
Total SI = 7 + 7 = 14 units.
Given 15 units = ₹450. Therefore, 1 unit = 30.
SI = 14 units = 14 × 30 = ₹420.

Question 4: Complex Fraction – 6 1/4%

Question: The difference between CI and SI for 2 years on a certain sum at 6 1/4% per annum is ₹20. What is the sum?

Analysis:

6 1/4% might look scary, but it is simply 25/4 % = 25/400 = 1/16. In the world of Previous Year Questions, this is a standard trap.

The 30-Second Ninja Shortcut:

Rate = 1/16. So x = 16.
We know for 2 years, Difference = Principal / x².
20 = Principal / 16²
20 = Principal / 256
Principal = 256 × 20 = ₹5,120.

Question 5: Effective Rate Comparison

Question: A fashion startup borrows money at 11 1/9% simple interest. Another startup borrows the same amount at the same rate but at compound interest. If after 2 years the second startup pays ₹100 more than the first, what was the loan amount?

The 30-Second Ninja Shortcut:

Rate = 11 1/9% = 1/9. Here x = 9.
The “₹100 more” is the Difference between CI and SI.
Difference = Principal / x²
100 = Principal / 9²
100 = Principal / 81
Principal = ₹8,100.

Cheat Sheet: 2-Year Interest Formulas (Rate = 1/x)

Summary and Final Strategy

In the NIFT GAT exam, time is your most precious resource. While the traditional formulas for Simple Interest and Compound Interest will eventually get you the answer, the fractional ninja methods we discussed today are what separate the top rankers from the rest.

Remember: Whenever you see a complex percentage in Previous Year Questions, your first instinct should be to convert it to a fraction. Once you have 1/x, the entire structure of the problem collapses into simple units. Practice these conversions until they become second nature!