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Numerical Ability is a core component of the Civil Service Exam, and work problems<\/strong> are among the most frequently tested and most confusing question types. These problems appear simple on the surface, but many examinees lose points due to poor understanding of concepts like work rate, time relationships, and efficiency.<\/p>\n This guide explains work problems step by step<\/strong>, from basic concepts to advanced variations, using clear logic rather than shortcuts that are easy to forget under exam pressure. By the end of this article, you should be able to solve work problems accurately and confidently.<\/p>\n Work problems generally involve people, machines, or groups completing a task over time. The goal is to determine how long the work takes<\/strong>, how many workers are needed<\/strong>, or how much work is done<\/strong> within a certain period.<\/p>\n Typical keywords include:<\/p>\n complete a job<\/em><\/p>\n<\/li>\n finish the work<\/em><\/p>\n<\/li>\n working together<\/em><\/p>\n<\/li>\n per day \/ per hour<\/em><\/p>\n<\/li>\n faster \/ slower<\/em><\/p>\n<\/li>\n<\/ul>\n These problems test your ability to:<\/p>\n Interpret rates correctly<\/p>\n<\/li>\n Set up equations logically<\/p>\n<\/li>\n Avoid common calculation traps<\/p>\n<\/li>\n<\/ul>\n At the heart of all work problems is a simple relationship:<\/p>\n Work = Rate \u00d7 Time<\/strong><\/p>\n Where:<\/p>\n Work<\/strong> is the total task (often treated as 1 whole job)<\/p>\n<\/li>\n Rate<\/strong> is the amount of work completed per unit of time<\/p>\n<\/li>\n Time<\/strong> is how long the work takes<\/p>\n<\/li>\n<\/ul>\n If one person completes a job in 10 days, their rate is:<\/p>\n 1 job \u00f7 10 days = 1\/10 job per day<\/strong><\/p>\n Understanding this idea is far more important than memorizing formulas.<\/p>\n These are the simplest form of work problems and often serve as the foundation for more complex questions.<\/p>\n A worker can complete a job in 8 days. How much work does the worker complete in 1 day?<\/p>\n Solution<\/strong><\/p>\n Total work = 1 job<\/p>\n<\/li>\n Time = 8 days<\/p>\n<\/li>\n Rate = 1 \u00f7 8 = 1\/8 job per day<\/strong><\/p>\n<\/li>\n<\/ul>\n This concept becomes critical when combining multiple workers later.<\/p>\n When workers work together, their rates add up<\/strong>, not their times.<\/p>\n Worker A can finish a job in 6 days. Step 1: Convert time into rate<\/strong><\/p>\n Worker A rate = 1\/6 job per day<\/p>\n<\/li>\n Worker B rate = 1\/12 job per day<\/p>\n<\/li>\n<\/ul>\n Step 2: Add rates<\/strong><\/p>\n Combined rate = 1\/6 + 1\/12<\/p>\n<\/li>\n Find common denominator: 1\/6 = 2\/12<\/p>\n<\/li>\n Combined rate = 2\/12 + 1\/12 = 3\/12 = 1\/4 job per day<\/p>\n<\/li>\n<\/ul>\n Step 3: Find time<\/strong><\/p>\n Time = 1 \u00f7 (1\/4) = 4 days<\/strong><\/p>\n<\/li>\n<\/ul>\n Many examinees mistakenly do this:<\/p>\n 6 days + 12 days = 18 days ❌<\/p>\n This is incorrect because time does not combine linearly. Only rates combine.<\/strong><\/p>\n Remember:<\/p>\n Work rates add<\/strong><\/p>\n<\/li>\n Time never adds directly<\/strong><\/p>\n<\/li>\n<\/ul>\n Not all workers are equally efficient. Some complete work faster than others.<\/p>\n A can do a job in 10 days, while B is twice as efficient as A. How long will B take to complete the same job?<\/p>\n Solution<\/strong><\/p>\n If B is twice as efficient, B works twice as fast<\/p>\n<\/li>\n A\u2019s rate = 1\/10 job per day<\/p>\n<\/li>\n B\u2019s rate = 2 \u00d7 (1\/10) = 1\/5 job per day<\/p>\n<\/li>\n<\/ul>\n Time for B<\/strong><\/p>\n Time = 1 \u00f7 (1\/5) = 5 days<\/strong><\/p>\n<\/li>\n<\/ul>\n Efficiency comparisons are common in the Civil Service Exam.<\/p>\n Sometimes a worker starts a job, then another finishes it.<\/p>\n A can complete a job in 12 days. A works for 4 days, then B completes the rest in 6 days. How long would B take to complete the whole job alone?<\/p>\n Step 1: Work done by A<\/strong><\/p>\n A\u2019s rate = 1\/12<\/p>\n<\/li>\n Work done in 4 days = 4 \u00d7 (1\/12) = 1\/3<\/p>\n<\/li>\n<\/ul>\n Step 2: Remaining work<\/strong><\/p>\n Remaining work = 1 \u2212 1\/3 = 2\/3<\/p>\n<\/li>\n<\/ul>\n Step 3: B\u2019s rate<\/strong><\/p>\n B finishes 2\/3 work in 6 days<\/p>\n<\/li>\n B\u2019s rate = (2\/3) \u00f7 6 = 2\/18 = 1\/9 job per day<\/p>\n<\/li>\n<\/ul>\n Step 4: Time for B alone<\/strong><\/p>\n Time = 1 \u00f7 (1\/9) = 9 days<\/strong><\/p>\n<\/li>\n<\/ul>\n These problems involve filling and emptying<\/strong>, which is still a work problem at its core.<\/p>\n A pipe fills a tank in 8 hours, while another pipe empties it in 12 hours. If both pipes are opened together, how long will it take to fill the tank?<\/p>\n Step 1: Rates<\/strong><\/p>\n Filling rate = 1\/8 tank per hour<\/p>\n<\/li>\n Emptying rate = \u22121\/12 tank per hour<\/p>\n<\/li>\n<\/ul>\n Step 2: Net rate<\/strong><\/p>\n Net rate = 1\/8 \u2212 1\/12<\/p>\n<\/li>\n Common denominator = 24<\/p>\n<\/li>\n Net rate = 3\/24 \u2212 2\/24 = 1\/24<\/p>\n<\/li>\n<\/ul>\n Step 3: Time<\/strong><\/p>\n Time = 1 \u00f7 (1\/24) = 24 hours<\/strong><\/p>\n<\/li>\n<\/ul>\n Sometimes work capacity is given in ratios.<\/p>\n 3 men can do the same work as 5 women. If 6 men work for 4 days, how many days will 10 women take to do the same work?<\/p>\n Step 1: Establish equivalence<\/strong><\/p>\n 3 men = 5 women<\/p>\n<\/li>\n 1 man = 5\/3 women<\/p>\n<\/li>\n<\/ul>\n Step 2: Convert work<\/strong><\/p>\n 6 men = 6 \u00d7 (5\/3) = 10 women<\/p>\n<\/li>\n<\/ul>\n Step 3: Compare time<\/strong><\/p>\n Same number of workers doing the same work<\/p>\n<\/li>\n Time required = 4 days<\/strong><\/p>\n<\/li>\n<\/ul>\n These questions combine work rates with proportional pay.<\/p>\n A and B work together for 10 days and earn \u20b14,000. A alone can complete the job in 20 days, while B alone can complete it in 30 days. How much should A receive?<\/p>\n Step 1: Rates<\/strong><\/p>\n A\u2019s rate = 1\/20<\/p>\n<\/li>\n B\u2019s rate = 1\/30<\/p>\n<\/li>\n<\/ul>\n Step 2: Ratio of work<\/strong><\/p>\n A : B = (1\/20) : (1\/30)<\/p>\n<\/li>\n Multiply by 60 \u2192 3 : 2<\/p>\n<\/li>\n<\/ul>\n Step 3: Divide wages<\/strong><\/p>\n Total = \u20b14,000<\/p>\n<\/li>\n A\u2019s share = 3\/5 \u00d7 4,000 = \u20b12,400<\/strong><\/p>\n<\/li>\n B\u2019s share = 2\/5 \u00d7 4,000 = \u20b11,600<\/p>\n<\/li>\n<\/ul>\n For some problems, especially under time pressure, you can use the LCM method<\/strong>.<\/p>\n A finishes a job in 4 days, B in 6 days. How long together?<\/p>\n Step 1: LCM of 4 and 6 = 12<\/strong><\/p>\n A\u2019s work per day = 12\/4 = 3 units<\/p>\n<\/li>\n B\u2019s work per day = 12\/6 = 2 units<\/p>\n<\/li>\n<\/ul>\n Step 2: Combined work<\/strong><\/p>\n Total per day = 3 + 2 = 5 units<\/p>\n<\/li>\n<\/ul>\n Step 3: Time<\/strong><\/p>\n Time = 12 \u00f7 5 = 2.4 days<\/strong><\/p>\n<\/li>\n<\/ul>\n Use this method only if you are comfortable with it.<\/p>\n Avoid these frequent mistakes:<\/p>\n Adding time instead of rates<\/p>\n<\/li>\n Forgetting to subtract emptying rates<\/p>\n<\/li>\n Misreading \u201ctwice as efficient\u201d as twice the time<\/p>\n<\/li>\n Ignoring partial work already completed<\/p>\n<\/li>\n Rushing without setting up equations<\/p>\n<\/li>\n<\/ul>\n Always convert time to rate first<\/strong><\/p>\n<\/li>\n Treat total work as 1 job<\/strong> unless stated otherwise<\/p>\n<\/li>\n Write rates clearly before calculating<\/p>\n<\/li>\n Estimate answers to catch mistakes<\/p>\n<\/li>\n Practice regularly under timed conditions<\/p>\n<\/li>\n<\/ul>\n Work problems are not about complex mathematics; they are about clear thinking and proper setup<\/strong>. Once you master the relationship between work, rate, and time, even the hardest-looking problems become manageable.<\/p>\n In the Civil Service Exam, accuracy matters more than speed. Build a strong foundation, practice systematically, and approach each problem with confidence and logic.<\/p>\n A can finish a job in 15 days. What fraction of the work does A complete in 1 day? A can finish a job in 18 days. How much work will A complete in 6 days? A finishes a job in 20 days. How long will A take to finish 35\\frac{3}{5}<\/span>5<\/span><\/span>3<\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> of the job?
\nUnderstanding Work Problems in the Civil Service Exam<\/h2>\n
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\nThe Core Concept: Work, Rate, and Time<\/h2>\n
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\nSingle Worker Work Problems<\/h2>\n
Example 1<\/h3>\n
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\nMultiple Workers Working Together<\/h2>\n
Example 2<\/h3>\n
Worker B can finish the same job in 12 days.
How long will they take if they work together?<\/p>\n\n
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\nCommon Mistake: Adding Time Instead of Rates<\/h2>\n
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\nDifferent Work Efficiency Levels<\/h2>\n
Example 3<\/h3>\n
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\nWork Problems Involving Partial Work<\/h2>\n
Example 4<\/h3>\n
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\nPipes and Cisterns (Work with Loss)<\/h2>\n
Example 5<\/h3>\n
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\nWork Problems with Men, Women, and Children<\/h2>\n
Example 6<\/h3>\n
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\nWork and Wages Problems<\/h2>\n
Example 7<\/h3>\n
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\nShortcut Method Using LCM (When Appropriate)<\/h2>\n
Example 8<\/h3>\n
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\nCommon Traps in Civil Service Exam Work Problems<\/h2>\n
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\nExam Tips for Solving Work Problems Faster<\/h2>\n
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\nFinal Thoughts<\/h2>\n
Problem Sets With Answer Keys<\/h2>\n
Problem Set 1: Basics of Work Rate<\/h2>\n
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Answer:<\/strong> 115\\frac{1}{15}<\/span>15<\/span><\/span>1<\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n<\/li>\n
Answer:<\/strong> 6\u00d7118=136 \\times \\frac{1}{18} = \\frac{1}{3}<\/span>6<\/span>\u00d7<\/span><\/span>18<\/span><\/span>1<\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span>=<\/span><\/span>3<\/span><\/span>1<\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n<\/li>\n
Answer:<\/strong> 35\u00d720=12\\frac{3}{5} \\times 20 = 12<\/span>5<\/span><\/span>