NIFT GAT Previous Year Questions: Mastering Ratios and Proportions in Textile Design

Introduction: Why Ratios Rule the Runway

For a NIFT GAT aspirant, Mathematics isn’t just about numbers; it is about the precision of a silhouette and the integrity of a fabric blend. One of the most recurring themes in the Quantitative Ability section involves the Application of Ratios and Proportions. Specifically, NIFT examiners love to test how you apply these concepts to textile blending (the science of mixing fibers) and pattern scaling (the art of resizing designs). This guide breaks down the core concepts and decodes actual patterns seen in Previous Year Questions to give you a competitive edge.

Question 1: The Complex Fiber Blend

Problem: A textile mill produces a special yarn by blending two types of materials. Material A contains Cotton and Polyester in the ratio 7:3. Material B contains Cotton and Polyester in the ratio 4:1. In what ratio should Material A and Material B be mixed to create a final blend where the ratio of Cotton to Polyester is 3:1?

The Traditional Method (The Long Way)

In the traditional approach, we calculate the fraction of cotton in each material.
Cotton in A = 7/10.
Cotton in B = 4/5.
Cotton in Final Blend = 3/4.
Let the amount of Material A used be ‘x’ and Material B be ‘y’.
Equation: (7/10)x + (4/5)y = (3/4)(x + y).
Multiplying by the LCM (20) to clear denominators: 14x + 16y = 15(x + y)
14x + 16y = 15x + 15y
16y – 15y = 15x – 14x
y = x, which means the ratio is 1:1.

The 30-Second Ninja Shortcut (Rule of Alligation)

Forget the long equations! Use Alligation on the Cotton fractions:
1. Cotton in A: 70% (7/10)
2. Cotton in B: 80% (4/5)
3. Target Cotton: 75% (3/4)
Subtract diagonally:
|80 – 75| = 5
|70 – 75| = 5
The ratio is 5:5, which simplifies to 1:1.

Question 2: Proportional Scaling of Patterns

Problem: A designer has a standard rectangular sleeve pattern measuring 20 cm in length and 12 cm in width. If the designer needs to scale the pattern up so that the width becomes 15 cm while maintaining the original proportions, what will be the new length of the sleeve?

The Traditional Method

We use the property of proportions: L1/W1 = L2/W2.
20 / 12 = L2 / 15.
Cross-multiplying: 12 * L2 = 20 * 15
12 * L2 = 300
L2 = 300 / 12 = 25 cm.

The 30-Second Ninja Shortcut (The Scale Factor)

Find the Scale Factor (SF) for the known dimension:
New Width / Old Width = 15 / 12 = 1.25.
Since the proportions remain the same, multiply the Old Length by the same SF:
20 * 1.25 = 25 cm.
Mentally: “15 is 12 plus one-fourth of 12. So, New Length is 20 plus one-fourth of 20 (5) = 25.”

Question 3: The Dye Concentration Mix

Problem: A master dyer has 40 liters of a 15% indigo dye solution. He wants to increase the concentration to 20% by adding a pure 100% indigo extract. How much pure extract must be added?

The Traditional Method

Let ‘x’ be the amount of pure dye added.
Current dye = 15% of 40 = 6 liters.
Total dye after addition = 6 + x.
Total volume after addition = 40 + x.
(6 + x) / (40 + x) = 20/100 = 1/5.
30 + 5x = 40 + x
4x = 10
x = 2.5 liters.

The 30-Second Ninja Shortcut (Concentration Ratio)

Use Alligation again!
Lower Concentration: 15%
Higher Concentration: 100%
Target: 20%
Difference 1: |100 – 20| = 80
Difference 2: |15 – 20| = 5
Ratio of (15% solution) to (100% dye) = 80 : 5 = 16 : 1.
If 16 parts = 40 liters, then 1 part = 40/16 = 2.5 liters.

Question 4: Fabric Shrinkage and Area Ratios

Problem: A specific linen fabric shrinks in a ratio of 10:9 along its length and 5:4 along its width after the first wash. If the original area of a fabric piece was 500 square cm, what is the area after washing?

The Traditional Method

Let original Length = L and original Width = W. L * W = 500.
New Length = (9/10)L.
New Width = (4/5)W.
New Area = (9/10)L * (4/5)W = (36/50) * (L * W).
New Area = (36/50) * 500 = 360 square cm.

The 30-Second Ninja Shortcut (Compound Ratio)

Area is a product of two linear dimensions. Simply multiply the ratios!
Shrinkage Factor = (9/10) * (4/5) = 36/50.
Final Area = 500 * (36/50) = 360 square cm.
In NIFT GAT, if you see two ratios affecting a single product, always use the Compound Ratio method.

Question 5: Gold Thread (Zari) Composition

Problem: In a luxury Banarasi silk, the ratio of Silk to Silver thread is 5:2 and the ratio of Silver thread to Gold thread is 3:1. If the total weight of the fabric is 400 grams (ignoring minor weights), how many grams of Gold thread are present?

The Traditional Method

We need a combined ratio of Silk : Silver : Gold.
Silk : Silver = 5 : 2
Silver : Gold = 3 : 1
To bridge them, make the ‘Silver’ value the same. LCM of 2 and 3 is 6.
Silk : Silver = 15 : 6
Silver : Gold = 6 : 2
Combined Ratio = 15 : 6 : 2.
Total parts = 15 + 6 + 2 = 23 parts.
Gold = (2 / 23) * 400 = 34.78 grams.

The 30-Second Ninja Shortcut (The Zig-Zag Multiply)

Write them vertically:
5 : 2
3 : 1
Multiply down-left (5*3=15), then across (2*3=6), then down-right (2*1=2).
Result: 15 : 6 : 2.
Sum = 23. Gold = (2/23) of 400.
If the total was 460 (common in Previous Year Questions for easier math), the answer would be exactly 40g.

Cheat Sheet: Quick Revision Formulas

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