Cracking the NIFT GAT: Mastering Work Intervals and Worker Efficiency

The General Ability Test (GAT) for the National Institute of Fashion Technology (NIFT) is not just about fashion; it is a test of your analytical speed and mathematical precision. Among the most frequent visitors in the Quantitative Ability section are ‘Time and Work’ problems. Specifically, NIFT loves to test your ability to handle dynamic scenarios where workers join or leave a task mid-way. These problems are designed to consume your time, but with the right decoding of Previous Year Questions, you can solve them in under 30 seconds. In this comprehensive guide, we will break down the complex logic of remaining work, efficiency ratios, and interval-based departures using the famous LCM (Least Common Multiple) method.

The Core Concept: The LCM Method vs. The Fractional Method

In school, we were taught the Fractional Method where if a person does a work in 10 days, their 1-day work is 1/10. While mathematically sound, adding fractions like 1/12 + 1/15 + 1/20 under exam pressure is a recipe for calculation errors. For NIFT GAT, we use the Total Work as LCM method. By assuming the total work is the LCM of the days given, we convert every worker’s capacity into ‘units per day’. This turns complex fractions into simple whole-number addition and subtraction.

Simulated Question 1: The Early Departure Scenario

Question: Ananya can complete a fashion sketch in 15 hours, while Rahul can complete it in 20 hours. They start working together, but Ananya leaves after 4 hours of work. What portion of the sketch is still remaining?

Traditional Method Breakdown:

1. Ananya’s 1-hour work = 1/15. Rahul’s 1-hour work = 1/20.
2. Combined 1-hour work = (1/15 + 1/20) = 7/60.
3. Work done in 4 hours = 4 * (7/60) = 28/60 = 7/15.
4. Remaining work = 1 – 7/15 = 8/15.

30-Second Ninja Shortcut (The Unit Method):

1. Total Work (LCM of 15, 20): 60 units.
2. Efficiencies: Ananya = 4 units/hr, Rahul = 3 units/hr.
3. Combined Efficiency: 7 units/hr.
4. Work done in 4 hours: 7 * 4 = 28 units.
5. Remaining Work: 60 – 28 = 32 units.
6. Portion Remaining: 32/60 = 8/15.

Simulated Question 2: The Late Joiner Dynamic

Question: Designer A can finish a collection in 12 days. Designer B can finish it in 18 days. Designer A starts the work alone and is joined by Designer B after 3 days. They work together for another 2 days. What is the remaining portion of the collection left to be completed?

Step-by-Step Logic:

1. Total Work (LCM of 12, 18): 36 units.
2. Efficiencies: A = 3 units/day, B = 2 units/day.
3. Initial Phase (A alone for 3 days): 3 units/day * 3 days = 9 units done.
4. Second Phase (A + B for 2 days): (3 + 2) units/day * 2 days = 10 units done.
5. Total Work Done: 9 + 10 = 19 units.
6. Remaining Work: 36 – 19 = 17 units.
7. Portion Remaining: 17/36.

Simulated Question 3: The Efficiency Ratio Departure

Question: P is 50% more efficient than Q. Q can complete a task in 30 days. P starts the work and leaves after 5 days. Then Q works for 10 days and also leaves. What portion of the task remains?

The Ninja Decoding:

1. Determine Efficiency Ratio: Efficiency P : Q = 150 : 100 = 3 : 2.
2. Calculate Total Work: Since Q (Efficiency 2) takes 30 days, Total Work = 2 * 30 = 60 units.
3. P’s Work (5 days): 3 units/day * 5 days = 15 units.
4. Q’s Work (10 days): 2 units/day * 10 days = 20 units.
5. Total Completed: 15 + 20 = 35 units.
6. Remaining Work: 60 – 35 = 25 units.
7. Portion Remaining: 25/60 = 5/12.

Simulated Question 4: The Three-Worker Chaos

Question: X, Y, and Z can complete a project in 10, 15, and 20 days respectively. All three start working together. After 2 days, X leaves. After another 2 days, Y leaves. What portion of the work is left for Z to finish alone?

Advanced Interval Breakdown:

1. Total Work (LCM 10, 15, 20): 60 units.
2. Efficiencies: X=6, Y=4, Z=3.
3. Day 1-2 (X+Y+Z): (6+4+3) * 2 = 13 * 2 = 26 units.
4. Day 3-4 (Y+Z only): (4+3) * 2 = 7 * 2 = 14 units.
5. Total work done so far: 26 + 14 = 40 units.
6. Remaining Work: 60 – 40 = 20 units.
7. Portion Remaining: 20/60 = 1/3.

Simulated Question 5: Negative Intervals (The Mistake Correction)

Question: A tailor can stitch a dress in 8 hours. His assistant can stitch it in 12 hours. They work together for 3 hours, but then the tailor realizes he made a mistake and unstitches 25% of the total work done so far. After this, the tailor leaves. What portion of the total task is still left for the assistant?

The Critical Logic:

1. Total Work (LCM 8, 12): 24 units.
2. Efficiencies: Tailor = 3, Assistant = 2.
3. 3 Hours Work: (3+2) * 3 = 15 units.
4. Mistake/Unstitching: 25% of 15 units = 3.75 units removed.
5. Effective Work Done: 15 – 3.75 = 11.25 units.
6. Remaining Portion: (24 – 11.25) / 24 = 12.75 / 24.
7. Simplified: 12.75 / 24 = 1275 / 2400 = 51 / 96 = 17/32.

Master Cheat Sheet: Quick Revision Formulas

• Always find the LCM of all time values given in the problem first.
• Never subtract people; subtract their efficiency from the total hourly/daily rate.
• Portion means the answer should always be a fraction between 0 and 1.

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