Mastering Time and Work: Previous Year Questions Decoder

Welcome, Kerala PSC aspirants! If you have been tracking the pattern of Secretariat Assistant, LDC, or VEO exams, you know that Time and Work is not just a topic—it is a scoring goldmine. Specifically, the questions where people ‘join’ or ‘leave’ midway are designed to consume your time and induce errors. This guide is curated by the experts at myentrance.in to help you decode these patterns using the legendary LCM method, moving away from the cumbersome fractional equations used in traditional schooling.

Understanding the relationship between efficiency, time, and total work is the key. In the competitive landscape of Kerala, where every mark counts, speed is your greatest ally. We will examine five distinct scenarios based on actual Previous Year Questions trends, breaking down why the shortcut works better than the long-form method.

Concept Deep Dive: The LCM Revolution

In standard textbooks, you are taught that if a person ‘A’ completes a work in 10 days, his one-day work is 1/10. When ‘B’ joins, you add 1/10 + 1/12… and suddenly you are drowning in cross-multiplications. The 30-Second Ninja Shortcut used by toppers replaces these fractions with ‘Units’.

Think of the ‘Total Work’ as a specific number of chairs to be built. If the LCM of 10 and 15 is 30, then the total work is 30 chairs. Now, math becomes simple addition and subtraction of whole numbers. This is the logic we will apply to the Previous Year Questions simulations below.

Question 1: The ‘Early Leaver’ Scenario

Scenario: A can complete a work in 20 days and B can do it in 30 days. They start working together, but A leaves after 5 days. In how many days will B finish the remaining work?

The Traditional Method (The Time-Waster)

Work done by A and B in 1 day = (1/20 + 1/30) = 5/60 = 1/12.
Work done in 5 days = 5 * (1/12) = 5/12.
Remaining work = 1 – 5/12 = 7/12.
Time taken by B to finish 7/12 work = (7/12) / (1/30) = (7/12) * 30 = 17.5 days.
This involves complex fraction handling which often leads to silly mistakes under exam pressure.

The 30-Second Ninja Shortcut (The Winner)

1. Find Total Work: LCM of 20 and 30 = 60 Units.
2. Efficiency: A = 60/20 = 3 units/day; B = 60/30 = 2 units/day.
3. Work done together: (3+2) = 5 units/day. In 5 days, they finish 5 * 5 = 25 units.
4. Remaining Work: 60 – 25 = 35 units.
5. B’s Time: 35 units / B’s efficiency (2) = 17.5 days.
Result: Same answer, but purely with simple integers!

Question 2: The ‘Late Joiner’ Scenario

Scenario: X can complete a project in 15 days. After working for 3 days alone, Y joins him, and they finish the rest in 4 more days. How many days would Y alone take to finish the whole work?

The 30-Second Ninja Shortcut

1. Assume Total Work: Let’s take a multiple of 15 and 4 (since we don’t know Y’s days). Let Total Work = 60 units.
2. X’s Efficiency: 60 / 15 = 4 units/day.
3. X’s Initial Work: In 3 days, X finished 4 * 3 = 12 units.
4. Remaining Work: 60 – 12 = 48 units.
5. Combined Speed: They finished 48 units in 4 days. So, (X+Y) efficiency = 48 / 4 = 12 units/day.
6. Y’s Efficiency: (X+Y) – X = 12 – 4 = 8 units/day.
7. Y’s Total Time: 60 units / 8 units/day = 7.5 days.
This reverse-calculation is a frequent pattern in Kerala PSC Graduate Level exams.

Question 3: The ‘Leaving Before Completion’ Trap

Scenario: P, Q, and R can do a work in 10, 20, and 30 days respectively. They start together, but P leaves 2 days before the work is completed. In how many days was the work finished?

The Shortcut: The ‘Don’t Let Them Leave’ Method

This is a classic ‘Previous Year Questions’ favorite. When someone leaves *before* completion, we pretend to force them to stay and add their potential work to the total.

1. Total Work (LCM of 10, 20, 30): 60 units.
2. Efficiencies: P = 6, Q = 3, R = 2.
3. The Logic: P left 2 days early. If P had stayed, he would have done (2 days * 6 efficiency) = 12 more units.
4. New Total: 60 + 12 = 72 units.
5. Combined Efficiency: 6 + 3 + 2 = 11.
6. Total Time: 72 / 11 = 6 and 6/11 days.
By ‘adding’ the work of the person who leaves early, we can treat them as if they stayed the whole time, simplifying the division!

Question 4: Mixed Joining and Leaving

Scenario: A can do a task in 12 days, B in 18 days. A starts the work. After 2 days, B joins him. After 3 more days, A leaves. How much more time does B take to finish?

Detailed Breakdown

1. Total Work (LCM 12, 18): 36 units.
2. Efficiencies: A = 3, B = 2.
3. Phase 1: A works alone for 2 days. Work = 3 * 2 = 6 units.
4. Phase 2: A and B work for 3 days. Work = (3+2) * 3 = 15 units.
5. Total Work done so far: 6 + 15 = 21 units.
6. Work left: 36 – 21 = 15 units.
7. Phase 3: B finishes 15 units. Time = 15 / 2 = 7.5 days.
Kerala PSC often uses these multi-step scenarios to test if you can track the progress meticulously.

Question 5: Alternating Joiners

Scenario: A can finish a work in 24 days. B is 20% more efficient than A. If A starts and B joins after 4 days, find the total time taken.

Solving with Efficiency Ratios

1. Determine Efficiency: If A’s efficiency is 100, B’s is 120. Ratio A:B = 5:6.
2. Total Work: Since A takes 24 days, Total Work = Efficiency * Time = 5 * 24 = 120 units.
3. Initial Progress: A works for 4 days: 5 * 4 = 20 units.
4. Remaining: 120 – 20 = 100 units.
5. Joint Effort: (5+6) = 11 units/day. Time = 100 / 11 = 9 and 1/11 days.
6. Total Time: 4 days (start) + 9 1/11 days = 13 1/11 days.

Cheat Sheet: Quick Revision Table

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