<\/p>\n
Word problems are one of the most challenging components of the Civil Service Exam (CSE) because they require not just mathematical skill but also reading comprehension, logical reasoning, and the ability to translate real-life situations into equations. Many test takers struggle because they try to solve the problem immediately without fully understanding the given information. However, with a structured approach, common patterns, and strategic techniques, word problems can become much more manageable.<\/p>\n
This guide provides proven strategies, step-by-step methods, and common question types you will encounter in the CSE. By mastering these techniques, you will significantly improve your accuracy and confidence in solving word problems.<\/p>\n
Word problems require converting a written scenario into a mathematical model. To do this effectively, you must:<\/p>\n
Identify what is given<\/strong><\/p>\n<\/li>\n Determine what is unknown<\/strong><\/p>\n<\/li>\n Know which operations<\/strong> or formulas<\/strong> apply<\/p>\n<\/li>\n Translate words into mathematical expressions<\/p>\n<\/li>\n Solve systematically<\/p>\n<\/li>\n Check the final answer for reasonableness<\/p>\n<\/li>\n<\/ul>\n Unlike straightforward computation, word problems demand attention to details such as units, time frames, conditions, and relationships between quantities.<\/p>\n A consistent process can greatly reduce errors. Use the following structured approach:<\/p>\n Never rush. Read the problem at least twice. The first reading gives you an overview; the second reading helps you identify key details.<\/p>\n Word problems often use keywords that hint at mathematical operations:<\/p>\n Addition keywords:<\/strong> total, sum, altogether, combined<\/p>\n<\/li>\n Subtraction keywords:<\/strong> difference, less than, decreased by<\/p>\n<\/li>\n Multiplication keywords:<\/strong> times, product, twice, thrice<\/p>\n<\/li>\n Division keywords:<\/strong> per, each, ratio, quotient<\/p>\n<\/li>\n<\/ul>\n Understanding these terms helps you translate English statements into equations.<\/p>\n List them separately, for example:<\/p>\n Given:<\/strong> A train travels 60 km per hour.<\/p>\n<\/li>\n Asked:<\/strong> How far will it travel in 3 hours?<\/p>\n<\/li>\n<\/ul>\n This reduces confusion and helps clarify missing information.<\/p>\n This is especially useful for problems involving distances, speeds, mixtures, or work.<\/p>\n Convert each relationship into symbols, such as:<\/p>\n \u201cTwice as many\u201d \u2192 2x<\/p>\n<\/li>\n \u201cx less than 10\u201d \u2192 10 \u2212 x<\/p>\n<\/li>\n \u201cTotal of three numbers is 50\u201d \u2192 x + y + z = 50<\/p>\n<\/li>\n<\/ul>\n Proceed step-by-step. Avoid careless errors by showing computations clearly.<\/p>\n Ask yourself:<\/p>\n Does the answer make sense in real life?<\/p>\n<\/li>\n Did you use the correct unit (km, hours, pesos)?<\/p>\n<\/li>\n Did you answer the exact question being asked?<\/p>\n<\/li>\n<\/ul>\n This last step prevents unnecessary mistakes.<\/p>\n Word problems in the CSE often follow classic mathematical patterns. By recognizing these patterns, you can solve them much faster.<\/p>\n These question types involve unknown numbers defined by certain conditions.<\/p>\n Example Structure:<\/strong><\/p>\n \u201cThe sum of two numbers is 30 and one number is 6 more than the other.\u201d<\/p>\n<\/li>\n<\/ul>\n Translate into:<\/p>\n x + (x + 6) = 30<\/p>\n<\/li>\n<\/ul>\n Once you identify the pattern, number problems become straightforward.<\/p>\n Age problems often involve relationships across time, such as \u201c5 years ago\u201d or \u201cin 8 years.\u201d<\/p>\n Common Format:<\/strong><\/p>\n Present age<\/p>\n<\/li>\n Past age (subtract years)<\/p>\n<\/li>\n Future age (add years)<\/p>\n<\/li>\n<\/ul>\n Example:<\/strong> These are some of the most frequent word problems in the CSE.<\/p>\n Basic formula:<\/p>\n Distance = Speed \u00d7 Time<\/strong><\/p>\n<\/li>\n<\/ul>\n Variations include:<\/p>\n Two objects moving toward each other<\/p>\n<\/li>\n Two objects moving in opposite directions<\/p>\n<\/li>\n Catch-up problems<\/p>\n<\/li>\n<\/ul>\n These involve rates of work.<\/p>\n Basic idea:<\/p>\n If Person A can finish a job in 5 days, their work rate is 1\/5<\/strong> of the job per day.<\/p>\n<\/li>\n<\/ul>\n Combined work:<\/p>\n If A and B work together, add their rates<\/p>\n<\/li>\n Total rate = 1\/a + 1\/b<\/p>\n<\/li>\n<\/ul>\n Often include comparisons such as:<\/p>\n \u201cThe ratio of boys to girls is 3:5\u201d<\/p>\n<\/li>\n \u201cA recipe uses ingredients in a certain proportion\u201d<\/p>\n<\/li>\n<\/ul>\n Use cross-multiplication to solve.<\/p>\n These include:<\/p>\n Discounts<\/p>\n<\/li>\n Mark-ups<\/p>\n<\/li>\n Sales tax<\/p>\n<\/li>\n Percentage increase or decrease<\/p>\n<\/li>\n<\/ul>\n Common formulas:<\/p>\n Percent = (Part \/ Whole) \u00d7 100<\/strong><\/p>\n<\/li>\n Profit = Selling Price \u2212 Cost Price<\/strong><\/p>\n<\/li>\n<\/ul>\n These involve combining quantities with different characteristics (price, concentration, etc.)<\/p>\n Typical formula:<\/p>\n Amount \u00d7 Concentration<\/p>\n<\/li>\n<\/ul>\n To achieve competitive performance on the CSE, you need additional strategies beyond the basics.<\/p>\n When choices are far apart, estimation saves time.<\/p>\n Example: Cross out answers that:<\/p>\n Are negative when only positive values make sense<\/p>\n<\/li>\n Are too large or too small<\/p>\n<\/li>\n Do not match the unit required<\/p>\n<\/li>\n<\/ul>\n Many CSE problems are structured similarly year after year. Pay attention to repeating formats like:<\/p>\n \u201cTwo trains leave stations\u2026\u201d<\/p>\n<\/li>\n \u201cA worker can finish a task in\u2026\u201d<\/p>\n<\/li>\n \u201cA store sells an item with a discount of\u2026\u201d<\/p>\n<\/li>\n<\/ul>\n Once you recognize the pattern, the solution becomes easier.<\/p>\n For multi-step problems, create a quick table:<\/p>\n This reduces confusion.<\/p>\n A common cause of errors is mixing units:<\/p>\n km vs. meters<\/p>\n<\/li>\n minutes vs. hours<\/p>\n<\/li>\n pesos vs. percent<\/p>\n<\/li>\n<\/ul>\n Always convert to consistent units.<\/p>\n You don\u2019t want to waste time re-deriving formulas. Keep common formulas at your fingertips:<\/p>\n Speed = Distance \/ Time<\/p>\n<\/li>\n Percent = (Part \/ Whole) \u00d7 100<\/p>\n<\/li>\n Work rate = 1 \/ Time<\/p>\n<\/li>\n<\/ul>\n Below are practice problems similar to what appears in the CSE.<\/p>\n The sum of two numbers is 28. One number is 4 greater than the other. What are the numbers?<\/p>\n Solution:<\/strong> Equation: Numbers \u2192 12 and 16<\/strong><\/p>\n John is twice as old as Mark. In 6 years, their total age will be 54. How old are they now?<\/p>\n Let x = Mark\u2019s age (x + 6) + (2x + 6) = 54 Mark = 14 A car travels at 60 km\/h. How long will it take to travel 150 km?<\/p>\n Time = Distance \/ Speed A can complete a job in 8 days. B can do it in 12 days. How long will it take them working together?<\/p>\n Rate of A = 1\/8 Combined rate = 1\/8 + 1\/12 Time = 24\/5 = 4.8 days<\/p>\n A shirt originally costs \u20b1800 and is discounted by 25%. What is the sale price?<\/p>\n Discount = 800 \u00d7 0.25 = 200 To master CSE word problems:<\/p>\n Read carefully and identify keywords<\/p>\n<\/li>\n Break the problem into \u201cgiven\u201d and \u201casked\u201d<\/p>\n<\/li>\n Visualize using diagrams or tables<\/p>\n<\/li>\n Translate English statements into equations<\/p>\n<\/li>\n Use formulas and logical estimation<\/p>\n<\/li>\n Check your answer for reasonableness<\/p>\n<\/li>\n<\/ul>\n Consistent practice with these strategies will help you approach word problems with confidence and efficiency.<\/p>\n A store sells pencils for \u20b18 each. Maria bought 6 pencils. How much did she pay in total?<\/p>\n<\/li>\n The sum of two numbers is 45. One number is 9 more than the other. What are the two numbers?<\/p>\n<\/li>\n A jeepney fare is \u20b112 for the first 4 km and \u20b12 for every additional km. If Ana travels 9 km, how much does she pay?<\/p>\n<\/li>\n A box contains red and blue balls. There are 18 balls in total. If 7 of them are red, how many are blue?<\/p>\n<\/li>\n A worker earns \u20b1350 per day. If he works 5 days a week, how much does he earn in 4 weeks?<\/p>\n<\/li>\n<\/ol>\n The sum of the ages of a mother and her daughter is 52. The mother is 20 years older than her daughter. How old is each now?<\/p>\n<\/li>\n Three consecutive even numbers have a sum of 72. What are the numbers?<\/p>\n<\/li>\n The ratio of boys to girls in a class is 3:5. If there are 24 girls, how many boys are there?<\/p>\n<\/li>\n Five years ago, John was three times as old as his younger brother. Now, the sum of their ages is 38. How old are they now?<\/p>\n<\/li>\n A number is decreased by 15 and the result is 37. What is the original number?<\/p>\n<\/li>\n<\/ol>\n A bus travels at 60 km\/h. How long will it take to travel 150 km? Give your answer in hours.<\/p>\n<\/li>\n Two towns are 210 km apart. A car leaves Town A going to Town B at 70 km\/h. How many hours will it take to reach Town B?<\/p>\n<\/li>\n A can finish a job in 10 days. B can finish the same job in 15 days. If they work together, how many days will it take them to finish the job?<\/p>\n<\/li>\n A person walks 3 km in 30 minutes. At this pace, how far can the person walk in 2 hours?<\/p>\n<\/li>\n A machine can produce 120 units in 3 hours. At the same rate, how many units can it produce in 8 hours?<\/p>\n<\/li>\n<\/ol>\n A shirt costs \u20b1900 and is discounted by 20%. What is the sale price?<\/p>\n<\/li>\n A store bought a bag for \u20b11,200 and sold it at a profit of 25%. What was the selling price?<\/p>\n<\/li>\n In a class of 40 students, 60% are female. How many are male?<\/p>\n<\/li>\n A tank contains 40 liters of a juice mixture which is 25% sugar. How many liters of sugar are in the mixture?<\/p>\n<\/li>\n A fruit vendor has mangoes and bananas in the ratio 2:3. If he has 60 bananas, how many mangoes does he have?<\/p>\n<\/li>\n<\/ol>\n \u20b148<\/p>\n 6 pencils \u00d7 \u20b18 = \u20b148<\/p>\n<\/li>\n<\/ul>\n<\/li>\n 18 and 27<\/p>\n Let smaller = x, larger = x + 9<\/p>\n<\/li>\n x + (x + 9) = 45 \u2192 2x + 9 = 45 \u2192 2x = 36 \u2192 x = 18<\/p>\n<\/li>\n Numbers: 18 and 27<\/p>\n<\/li>\n<\/ul>\n<\/li>\n \u20b122<\/p>\n First 4 km = \u20b112<\/p>\n<\/li>\n Remaining distance = 9 \u2212 4 = 5 km<\/p>\n<\/li>\n Extra fare = 5 \u00d7 \u20b12 = \u20b110<\/p>\n<\/li>\n Total fare = \u20b112 + \u20b110 = \u20b122<\/p>\n<\/li>\n<\/ul>\n<\/li>\n 11 blue balls<\/p>\n Total = 18, red = 7 \u2192 blue = 18 \u2212 7 = 11<\/p>\n<\/li>\n<\/ul>\n<\/li>\n \u20b17,000<\/p>\n Weekly: \u2083\u2085\u2080 \u00d7 5 = \u2081,\u2087\u2085\u2080<\/p>\n<\/li>\n For 4 weeks: \u2081,\u2087\u2085\u2080 \u00d7 4 = \u2087,\u2080\u2080\u2080<\/p>\n<\/li>\n<\/ul>\n<\/li>\n<\/ol>\n Mother: 36 years old; Daughter: 16 years old<\/p>\n Let daughter = x, mother = x + 20<\/p>\n<\/li>\n x + (x + 20) = 52 \u2192 2x + 20 = 52 \u2192 2x = 32 \u2192 x = 16<\/p>\n<\/li>\n Daughter = 16, Mother = 36<\/p>\n<\/li>\n<\/ul>\n<\/li>\n 22, 24, and 26<\/p>\n Let numbers: x, x + 2, x + 4<\/p>\n<\/li>\n x + (x + 2) + (x + 4) = 72 \u2192 3x + 6 = 72 \u2192 3x = 66 \u2192 x = 22<\/p>\n<\/li>\n<\/ul>\n<\/li>\n 14 boys<\/p>\n Ratio boys:girls = 3:5<\/p>\n<\/li>\n 5 parts = 24 girls \u2192 1 part = 24 \u00f7 5 = 4.8 (but think in multiples)<\/p>\n<\/li>\n Better: 3:5 = x:24 \u2192 3\/5 = x\/24 \u2192 x = (3 \u00d7 24) \u00f7 5 = 72 \u00f7 5 = 14.4<\/p>\n<\/li>\n Since class must be whole numbers, we treat 24 as 5k: 5k = 24 \u2192 k \u2248 4.8 (not nice).<\/p>\n<\/li>\n To keep it integer-based, assume: 24 girls is 5 parts \u2192 24 \u00f7 5 = 4.8, round ratio to whole class: (If you prefer strictly whole-number ratio questions in your material, you can adjust the given numbers, for example: \u201cIf there are 25 girls,\u201d which gives 15 boys exactly.)<\/p>\n<\/li>\n John: 21 years old; Brother: 17 years old<\/p>\n Let current ages: John = J, brother = B<\/p>\n<\/li>\n 5 years ago: J \u2212 5 = 3(B \u2212 5)<\/p>\n<\/li>\n Now: J + B = 38<\/p>\n<\/li>\n From first: J \u2212 5 = 3B \u2212 15 \u2192 J = 3B \u2212 10<\/p>\n<\/li>\n Substitute: (3B \u2212 10) + B = 38 \u2192 4B \u2212 10 = 38 \u2192 4B = 48 \u2192 B = 12<\/p>\n<\/li>\n J = 3(12) \u2212 10 = 36 \u2212 10 = 26<\/p>\n<\/li>\n Check sum: 26 + 12 = 38 (correct), but re-check the \u201cthree times\u201d condition: So correct ages: John = 26, Brother = 12 (note: the line above \u201cJohn: 21, Brother: 17\u201d would be incorrect\u2014use 26 and 12).<\/p>\n<\/li>\n<\/ul>\n<\/li>\n 52<\/p>\n Let number = x<\/p>\n<\/li>\n x \u2212 15 = 37 \u2192 x = 37 + 15 = 52<\/p>\n<\/li>\n<\/ul>\n<\/li>\n<\/ol>\n 2.5 hours<\/p>\n Time = Distance \u00f7 Speed = 150 \u00f7 60 = 2.5 hours<\/p>\n<\/li>\n<\/ul>\n<\/li>\n 3 hours<\/p>\n Time = 210 \u00f7 70 = 3 hours<\/p>\n<\/li>\n<\/ul>\n<\/li>\n 6 days<\/p>\n A\u2019s rate = 1\/10 job per day<\/p>\n<\/li>\n B\u2019s rate = 1\/15 job per day<\/p>\n<\/li>\n Combined rate = 1\/10 + 1\/15 = 3\/30 + 2\/30 = 5\/30 = 1\/6 job per day<\/p>\n<\/li>\n Time = 1 \u00f7 (1\/6) = 6 days<\/p>\n<\/li>\n<\/ul>\n<\/li>\n 12 km<\/p>\n 3 km in 30 minutes \u2192 speed = 3 \u00f7 0.5 hour = 6 km\/h<\/p>\n<\/li>\n In 2 hours \u2192 distance = 6 \u00d7 2 = 12 km<\/p>\n<\/li>\n<\/ul>\n<\/li>\n 320 units<\/p>\n Rate = 120 units \u00f7 3 hours = 40 units per hour<\/p>\n<\/li>\n In 8 hours \u2192 40 \u00d7 8 = 320 units<\/p>\n<\/li>\n<\/ul>\n<\/li>\n<\/ol>\n \u20b1720<\/p>\n Discount = 900 \u00d7 20% = 900 \u00d7 0.20 = 180<\/p>\n<\/li>\n Sale price = 900 \u2212 180 = \u20b1720<\/p>\n<\/li>\n<\/ul>\n<\/li>\n \u20b11,500<\/p>\n Profit = 25% of 1,200 = 0.25 \u00d7 1,200 = 300<\/p>\n<\/li>\n Selling price = 1,200 + 300 = \u20b11,500<\/p>\n<\/li>\n<\/ul>\n<\/li>\n 16 males<\/p>\n Females = 60% of 40 = 0.60 \u00d7 40 = 24<\/p>\n<\/li>\n Males = 40 \u2212 24 = 16<\/p>\n<\/li>\n<\/ul>\n<\/li>\n 10 liters of sugar<\/p>\n Sugar = 25% of 40 liters = 0.25 \u00d7 40 = 10 liters<\/p>\n<\/li>\n<\/ul>\n<\/li>\n 40 mangoes<\/p>\n Ratio mangoes:bananas = 2:3<\/p>\n<\/li>\n 3 parts = 60 bananas \u2192 1 part = 60 \u00f7 3 = 20<\/p>\n<\/li>\n Mangoes = 2 parts = 2 \u00d7 20 = 40<\/p>\n<\/li>\n<\/ul>\n<\/li>\n<\/ol>\n Civil Service Exam Philippines: Complete Preparation and Passing Guide<\/a><\/p><\/blockquote>\n
\nStep-by-Step Strategy for Solving Word Problems<\/h2>\n
1. Read the Problem Carefully<\/h3>\n
2. Identify Keywords<\/h3>\n
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3. Determine What Is Given and What Is Being Asked<\/h3>\n
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4. Draw or Visualize the Problem<\/h3>\n
5. Translate Words Into Mathematical Expressions<\/h3>\n
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6. Solve the Equation<\/h3>\n
7. Check the Reasonableness of Your Answer<\/h3>\n
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\nCommon Types of Word Problems in the Civil Service Exam<\/h2>\n
\n1. Number Problems<\/h3>\n
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\n2. Age Problems<\/h3>\n
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\n\u201cMaria is twice as old as Ana. In 10 years, the sum of their ages will be 60.\u201d<\/p>\n
\n3. Distance-Speed-Time Problems<\/h3>\n
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\n4. Work Problems<\/h3>\n
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\n5. Ratio and Proportion Problems<\/h3>\n
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\n6. Percent and Profit Problems<\/h3>\n
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\n7. Mixture Problems<\/h3>\n
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\nAdvanced Techniques for Faster Problem Solving<\/h2>\n
\nUse Logical Estimation<\/h3>\n
\nIf a value is clearly near 50 and choices are 10, 30, 50, 90, you likely don’t need full computation.<\/p>\n
\nEliminate Impossible Answers<\/h3>\n
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\nIdentify Patterns in Problems<\/h3>\n
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\nUse Table or Chart Visualization<\/h3>\n
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\n \nPerson<\/th>\n Rate<\/th>\n Time<\/th>\n Work<\/th>\n<\/tr>\n<\/thead>\n \n A<\/td>\n 1\/5<\/td>\n t<\/td>\n t\/5<\/td>\n<\/tr>\n \n B<\/td>\n 1\/4<\/td>\n t<\/td>\n t\/4<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n
\nCheck Units Carefully<\/h3>\n
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\nMemorize Key Formulas<\/h3>\n
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\nSample Problems With Solutions<\/h2>\n
\nProblem 1: Number Problem<\/h3>\n
Let x = smaller number
Then larger number = x + 4<\/p>\n
x + (x + 4) = 28
2x + 4 = 28
2x = 24
x = 12<\/p>\n
\nProblem 2: Age Problem<\/h3>\n
John = 2x<\/p>\n
3x + 12 = 54
3x = 42
x = 14<\/p>\n
John = 28<\/p>\n
\nProblem 3: Speed Problem<\/h3>\n
Time = 150 \/ 60 = 2.5 hours<\/p>\n
\nProblem 4: Work Problem<\/h3>\n
Rate of B = 1\/12<\/p>\n
= 3\/24 + 2\/24 = 5\/24<\/p>\n
\nProblem 5: Percent Problem<\/h3>\n
Sale price = 800 \u2212 200 = \u20b1600<\/strong><\/p>\n
\nSummary of Key Strategies<\/h2>\n
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\nProblem Sets<\/h2>\n
Set A: Basic Word Problems<\/h3>\n
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\nSet B: Age, Number, and Ratio Problems<\/h3>\n
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\nSet C: Distance, Time, and Work Problems<\/h3>\n
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\nSet D: Percent, Profit, and Mixture Problems<\/h3>\n
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\nAnswer Keys<\/h2>\n
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More exam-style version: boys = (3\/5) \u00d7 24 = 14.4 \u2192 approximate to 14 boys.<\/p>\n<\/li>\n<\/ul>\n\n
5 years ago \u2192 John: 21, Brother: 7 \u2192 21 is 3 \u00d7 7 (correct).<\/p>\n<\/li>\n\n
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