ETN News | TNPSC Group IV – Day 11 Date: 23 October 2026 | Time: 4:00 PM IST | Category: TNPSC Grp IV Subject: Aptitude & Mental Ability Title: Time and Work – Basic Rules, Shortcuts and 8 Fully Worked Examples
1. What Is Time and Work? Time and Work questions examine how long a person or group takes to complete a task. The key idea is to calculate the fraction of the task completed per unit of time. Time and Work appears in the official TNPSC Group IV aptitude syllabus. This session contains aptitude only, not General Studies.
2. Important Terms Total work: The entire job, represented by 1 or a convenient number of units (often the LCM of the given times). Work rate: The fraction of the job completed per day or hour. Efficiency: How much work a person completes in a given time. Time: The days or hours needed to finish the job.
3. Rules and Formulas (1) If A finishes a job in x days, A's one-day work = 1/x. (2) If A and B take x and y days individually, their combined one-day work = 1/x + 1/y. (3) Together, they finish in xy/(x+y) days, provided both work continuously on the same job. (4) If A+B finish in t days and A alone in x days, B's one-day work = 1/t − 1/x. The result must be positive. (5) For a fixed job, efficiency × time is constant. Efficiency and time are inversely proportional. (6) For equal work, identical worker efficiency and equal daily working hours: workers × days is constant. (7) Wages should be shared in proportion to actual work done. If people work for the same time, the wage ratio equals their work-rate ratio.
4. Fast LCM Method If A needs 12 days and B needs 18 days, take the whole job as LCM(12,18) = 36 units. A completes 3 units per day; B completes 2 units per day. Together they complete 5 units per day. Time = 36/5 = 7.2 days. This avoids complicated fractions.
5. Eight Fully Worked Examples
Example 1 – Two people working together A completes a job in 12 days and B in 18 days. How long together? A's one-day work = 1/12; B's = 1/18. Combined rate = 1/12 + 1/18 = (3+2)/36 = 5/36. Time = 36/5 = 7.2 days. Answer: 7.2 days.
Example 2 – Direct shortcut A needs 15 days and B needs 10 days. How long together? Time = (15 × 10)/(15+10) = 150/25 = 6. Answer: 6 days.
Example 3 – Find an individual's time A and B together finish in 8 days. A alone needs 12 days. How long does B alone need? B's one-day work = 1/8 − 1/12 = (3−2)/24 = 1/24. Answer: B alone needs 24 days.
Example 4 – One worker starts early A needs 10 days and B needs 15 days. A works alone for 2 days, and then both work together. Find total time. Work completed by A in 2 days = 2/10 = 1/5. Remaining work = 4/5. Combined rate = 1/10 + 1/15 = 1/6 per day. Time to finish remaining work = (4/5) ÷ (1/6) = 24/5 = 4.8 days. Total time = 2 + 4.8 = 6.8 days. Answer: 6.8 days.
Example 5 – Three workers A, B and C need 12, 15 and 20 days individually. How long together? LCM(12,15,20) = 60 units. Daily work: A = 5 units; B = 4 units; C = 3 units. Together = 12 units per day. Time = 60/12 = 5 days. Answer: 5 days.
Example 6 – Comparing efficiency A needs 20 days. B is 25% more efficient than A. How long does B need? B's rate = A's rate × 1.25. B's time = 20/1.25 = 16 days. Answer: 16 days. Greater efficiency means less time for the same work.
Example 7 – Workers and days Eight workers finish a job in 15 days. How long will 12 equally efficient workers take if daily working hours remain the same? 8 × 15 = 12 × x. x = 120/12 = 10 days. Answer: 10 days.
Example 8 – Sharing wages A alone can finish a job in 10 days and B alone in 15 days. They work together for the same duration and earn ₹2,500. Divide the wages. Work-rate ratio = (1/10):(1/15) = 3:2. A's share = 2500 × 3/5 = ₹1,500. B's share = 2500 × 2/5 = ₹1,000. Answer: A gets ₹1,500; B gets ₹1,000.
6. Common Mistakes Do not add the numbers of days directly; add work rates instead. Being 25% more efficient does not mean taking 25% less time. If a second worker joins later, subtract the work already completed before calculating the remaining time. The workers × days shortcut assumes equal efficiency and equal daily working hours.
7. One-Minute Revision x days to finish → one-day work = 1/x. Two workers → 1/x + 1/y. Time together → xy/(x+y). One worker's rate → combined rate minus the other worker's rate. Higher efficiency → shorter time for the same job. The LCM-units method is a useful shortcut.
8. Textbook Reference and Book-Back Tracking Relevant textbook: Tamil Nadu Samacheer Kalvi, Class 8 Mathematics, Chapter 4 – Life Mathematics, Time and Work. A secondary solution index identifies Exercise 4.4 on printed pages 150–151. That secondary index lists Question 1(i)–1(v) and Questions 2–10, giving 14 identifiable question parts. This is only a provisional inventory: the original government textbook, edition and completeness have not yet been checked against it. Verified original book-back questions completed: 0. Provisionally identified question parts: 14; official-source verification pending. Proposed evening batches: 1/3 = 1(i)–1(v); 2/3 = 2–6; 3/3 = 7–10. They will be labelled 'verified book-back' only after original-textbook verification. 2026–27 textbook edition: source not yet verified. Today's eight examples are original worked models, not authenticated TNPSC PYQs or verified textbook book-back questions.
9. Spaced Revision +1 day: 24 October 2026. +3 days: 26 October 2026. +7 days: 30 October 2026. +14 days: 6 November 2026. Also review yesterday's Simple Interest lesson today (+1-day review).
10. ETN Push Notification Title: 🔢 TNPSC Group IV | Time and Work – Day 11! Message: Learn two-worker and three-worker problems, LCM shortcuts, efficiency and wage sharing through 8 fully worked examples in today's 4 PM Aptitude lesson!
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