Mastering Weighted Average for NIFT GAT: The Ultimate Production & Labor Guide
Welcome, future designers and fashion managers! As you prepare for the National Institute of Fashion Technology (NIFT) General Ability Test (GAT), one topic consistently appears as a bridge between pure mathematics and practical industry application: Weighted Average. Unlike the simple average you learned in middle school, the weighted average is the lifeblood of garment manufacturing units. Whether you are calculating the average cost of a blended fabric or determining the mean labor hours required for a mixed batch of shirts and trousers, this concept is non-negotiable.
In this comprehensive decoder, we will break down the most complex Previous Year Questions from the NIFT GAT archives, specifically focusing on production costs and labor hours. By the end of this guide, you will not only understand the ‘Why’ behind these numbers but also the ‘How’ using our exclusive 30-Second Ninja Shortcuts.
💡 Why is Weighted Average crucial for NIFT?
NIFT tests your ability to think like a manager. In fashion, different inputs (like silk vs. cotton) have different quantities and prices. A simple average would ignore these proportions, leading to massive financial errors in the factory! Weighted Average gives more ‘weight’ to items with higher quantities, providing a realistic cost or time estimate.
Understanding the Core Mathematical Framework
Before jumping into Previous Year Questions, let’s solidify the formula. The weighted average is calculated by taking the sum of the products of each value and its corresponding weight, divided by the total sum of the weights.
Formula: Weighted Average = (w1v1 + w2v2 + … + wnvn) / (w1 + w2 + … + wn)
Where w = weight (quantity/hours) and v = value (cost/productivity).
Section 1: Fabric Production Costs
Question 1: A garment export house purchases 400 meters of premium linen at 1200 per meter and 600 meters of blended cotton at 400 per meter. What is the average cost per meter for the entire procurement?
The Traditional Method:
1. Calculate total cost for linen: 400 x 1200 = 4,80,000.
2. Calculate total cost for cotton: 600 x 400 = 2,40,000.
3. Total expenditure: 4,80,000 + 2,40,000 = 7,20,000.
4. Total quantity: 400 + 600 = 1000 meters.
5. Average Cost: 7,20,000 / 1000 = 720 per meter.
The 30-Second Ninja Shortcut (Ratio Method):
1. Simplify the weights (quantities): 400 : 600 simplifies to 2 : 3.
2. Multiply ratios by their costs: (2 x 1200) + (3 x 400) = 2400 + 1200 = 3600.
3. Divide by the sum of ratios: 3600 / (2 + 3) = 3600 / 5 = 720.
Why this works: Ratios eliminate large numbers, reducing the risk of calculation errors!
💡 Pro-Tip: The Alligation Cross
If you are given the average and need to find the quantity ratio, use the Alligation Cross. Subtract the average from the higher price and the lower price from the average to get the ratio instantly!
Section 2: Labor Hours and Manpower Efficiency
Question 2: In a boutique, 5 senior tailors work 8 hours a day with an efficiency of 4 garments per hour, while 10 junior tailors work 6 hours a day with an efficiency of 2 garments per hour. What is the weighted average production of garments per tailor per day?
The Traditional Method:
1. Senior total: 5 tailors x 8 hours x 4 garments = 160 garments.
2. Junior total: 10 tailors x 6 hours x 2 garments = 120 garments.
3. Total garments = 280.
4. Total tailors = 15.
5. Average = 280 / 15 = 18.67 garments/tailor.
The 30-Second Ninja Shortcut (Weighted Average of Daily Rates):
1. Daily rate for Senior: 8 x 4 = 32 garments.
2. Daily rate for Junior: 6 x 2 = 12 garments.
3. Weights are the number of tailors: 5 (Senior) and 10 (Junior). Ratio = 1:2.
4. (1 x 32 + 2 x 12) / (1 + 2) = (32 + 24) / 3 = 56 / 3 = 18.67.
Key Takeaway: Always identify what your ‘weight’ is. Here, the number of tailors acts as the weight.
Section 3: Blended Costs in Textile Mixes
Question 3: A designer creates a fabric blend using 3 parts of organic silk costing 1500/kg and 2 parts of recycled polyester costing 500/kg. What is the cost of 5kg of this blended fabric?
The Traditional Method:
Since the ratio is 3:2, for 5kg, we use 3kg silk and 2kg polyester.
Total Cost = (3 x 1500) + (2 x 500) = 4500 + 1000 = 5500.
Cost per kg = 5500 / 5 = 1100.
Total for 5kg = 5500.
The Ninja Trick (Deviation Method):
1. Assume a base price between 500 and 1500, say 1000.
2. Silk is +500 from base. Polyester is -500 from base.
3. Net deviation = (3 parts x +500) + (2 parts x -500) = +1500 – 1000 = +500.
4. Average deviation = +500 / (3+2) = +100.
5. Final Average = Base + Average Deviation = 1000 + 100 = 1100 per kg.
💡 Why use the Deviation Method?
When the numbers are huge (e.g., prices like 12540 and 13680), calculating total sums is a nightmare. Picking a base number and calculating small deviations is much faster!
Section 4: Complex Multi-Unit Production
Question 4: A manufacturing unit has three departments. Dept A (20 workers) earns an average of 500/day. Dept B (30 workers) earns an average of 600/day. Dept C (50 workers) earns an average of 450/day. What is the average daily wage of the unit?
The Traditional Method:
Total wages = (20×500) + (30×600) + (50×450) = 10,000 + 18,000 + 22,500 = 50,500.
Total workers = 20 + 30 + 50 = 100.
Average = 50,500 / 100 = 505/day.
The Ninja Shortcut:
1. Simplify worker ratios: 20:30:50 -> 2:3:5.
2. Use the Deviation Method (Base = 500).
3. Dept A deviation: 2 x 0 = 0.
4. Dept B deviation: 3 x (+100) = +300.
5. Dept C deviation: 5 x (-50) = -250.
6. Net: +50. Average deviation: 50 / (2+3+5) = +5.
7. Final Average: 500 + 5 = 505.
Section 5: Missing Weight Challenges
Question 5: The average cost of a designer collection of 10 dresses is 5000. If 6 dresses are luxury silk (avg 7000), what is the average cost of the remaining 4 cotton dresses?
The Traditional Method:
1. Total value of 10 dresses = 10 x 5000 = 50,000.
2. Total value of 6 silk dresses = 6 x 7000 = 42,000.
3. Value of remaining 4 dresses = 50,000 – 42,000 = 8,000.
4. Average of cotton dresses = 8,000 / 4 = 2000.
The Ninja Shortcut (Balance Method):
1. The luxury dresses are 2000 above the average (7000 – 5000 = 2000).
2. Total ‘surplus’ = 6 x 2000 = +12,000.
3. This surplus must be balanced by the ‘deficit’ of the 4 cotton dresses.
4. Deficit per cotton dress = 12,000 / 4 = 3000.
5. Cotton average = Target Average – Deficit = 5000 – 3000 = 2000.
Cheat Sheet: Weighted Average Formulae
| Concept | Formula / Trick |
|---|---|
| Standard Weighted Average | Sum of (W * V) / Total W |
| Ratio Simplification | Always simplify quantities (weights) before multiplying to save time. |
| Deviation Method | Assumed Mean + (Net Deviation / Total Weights) |
| Balance Method | Total Surplus = Total Deficit (Useful for finding missing values) |
Ready to Ace the NIFT GAT?
Understanding these mathematical nuances is what separates the top rankers from the rest. At MyEntrance, we specialize in converting complex Previous Year Questions into simple, actionable strategies. If you found these shortcuts helpful, imagine what our full mock test series can do for you!
💬 Chat with our Experts on WhatsApp (+91 9526806124)
