<\/p>\n
Percentages and discounts are among the most frequently tested topics in the Civil Service Exam (CSE). These questions appear in the Numerical Ability or Quantitative section and require examinees to understand how percentages work, how to convert fractions and decimals into percentages, how to compute increase or decrease, and how to determine the final price after a discount. Mastering these concepts significantly improves your calculation accuracy and speed, which are crucial during the exam.<\/p>\n
This guide provides a clear breakdown of all major ideas related to percentages and discounts, including practical examples, step-by-step solutions, and techniques to avoid common mistakes. Whether you are reviewing for the CSE Professional or Sub-Professional level, this guide builds the foundation you need to handle numerical problems with confidence.<\/p>\n
A percentage represents a fraction out of 100. The symbol %<\/strong> means \u201cper hundred.\u201d<\/p>\n For example:<\/p>\n Percentages allow comparisons even when quantities differ. This is why many exam questions use percentages to measure growth, reduction, profit, loss, and discounts.<\/p>\n Understanding conversions is essential for solving percentage questions quickly.<\/p>\n Multiply the fraction by 100%.<\/p>\n Example: (3\/5) \u00d7 100 = 60%<\/p>\n Multiply the decimal by 100.<\/p>\n Example: 0.45 \u00d7 100 = 45%<\/strong><\/p>\n Divide by 100.<\/p>\n Example: 72% \u00f7 100 = 0.72<\/strong><\/p>\n Write the percentage over 100 and simplify.<\/p>\n Example: 40% = 40\/100 = 2\/5<\/p>\n These conversions help you switch forms quickly depending on what the problem requires.<\/p>\n Use the formula:<\/p>\n Percentage of a number = Rate \u00d7 Base<\/strong><\/p>\n Where:<\/p>\n Example: 25% = 0.25 Percentage increase and decrease questions frequently appear in the exam. These questions involve comparing the old value with the new value.<\/p>\n Percentage Increase = ((New Value \u2013 Old Value) \/ Old Value) \u00d7 100<\/p>\n Percentage Decrease = ((Old Value \u2013 New Value) \/ Old Value) \u00d7 100<\/p>\n Example (Increase):<\/strong> ((260 \u2212 200) \/ 200) \u00d7 100 = 30%<\/p>\n Example (Decrease):<\/strong> ((500 \u2212 400) \/ 500) \u00d7 100 = 20%<\/p>\n A discount<\/strong> is a reduction from the original price. It is usually expressed as a percentage.<\/p>\n Discount Amount = Original Price \u00d7 Discount Rate<\/strong><\/p>\n Sale Price = Original Price \u2212 Discount Amount<\/strong><\/p>\n Example:<\/strong> Step 1: Compute discount amount. Step 2: Subtract from original. Stores sometimes offer multiple discounts, such as \u201c20% off, then an additional 10% off.\u201d These are not<\/strong> added directly.<\/p>\n You must apply the second discount to the already discounted price<\/strong>.<\/p>\n Example:<\/strong> Step 1: Apply 20% discount Step 2: Apply 10% discount Sometimes the problem gives the sale price after discount, and you need to find the original price.<\/p>\n Formula:<\/p>\n Original Price = Sale Price \u00f7 (1 \u2212 Discount Rate)<\/strong><\/p>\n Example:<\/strong> Original Price = 720 \u00f7 0.80 = 900 If the original price and sale price are known, you can find the discount rate.<\/p>\n Formula:<\/p>\n Discount Rate = ((Original Price \u2212 Sale Price) \/ Original Price) \u00d7 100<\/strong><\/p>\n Example:<\/strong> Discount = 1,500 \u2212 1,200 = 300 Percentage and discount problems often appear in situations such as:<\/p>\n CSE examiners design questions that require quick mental math, so understanding shortcuts is essential.<\/p>\n Move the decimal one place to the left. Example: 5% of 450 = half of 45 = 22.5<\/p>\n Example: 1% of 450 = 4.5<\/p>\n Example: 16% of 250 = 10% + 5% + 1%<\/p>\n Total = 25 + 12.5 + 2.5 = 40<\/p>\n What is 12% of 850?<\/p>\n 12% = 0.12 A price increases from \u20b1900 to \u20b11,080. What is the percentage increase?<\/p>\n Increase = 1,080 \u2212 900 = 180 A laptop costing \u20b135,000 is discounted by 18%. What is the sale price?<\/p>\n Discount = 18% of 35,000 = 0.18 \u00d7 35,000 = 6,300 After a 25% discount, a gadget sells for \u20b13,600. What was the original price?<\/p>\n Original Price = 3,600 \u00f7 0.75 = \u20b14,800<\/strong><\/p>\n A store applies two successive discounts of 30% and 20% on a \u20b15,000 item. What is the final price?<\/p>\n First discount: Second discount: Percentage and discount questions:<\/p>\n If you master basic percentage calculations and discount logic, you can answer these questions in less than 20 seconds each, leaving more time for difficult items.<\/p>\n Instructions:<\/strong> What is 18% of 250?<\/strong> What is 7.5% of 800?<\/strong> What percent of 400 is 80?<\/strong> A value increases from 1,200 to 1,500. What is the percentage increase? A quantity decreases from 960 to 720. What is the percentage decrease? A shirt costs \u20b1900 and is on sale at 15% discount. What is the sale price? A pair of shoes costs \u20b12,500. During a sale, it is given a 20% discount followed by an additional 10% discount on the reduced price. What is the final price? After a 30% discount, a bag is sold for \u20b11,750. What was its original price? A gadget\u2019s marked price is \u20b18,000. It is sold for \u20b16,000. What is the discount rate? A store advertises \u201cBuy now and save 12.5%!\u201d If the original price of a rice cooker is \u20b13,200, how much is the discount amount? A student scored 36 out of 45 in a quiz. What is her score in percent? (Round to the nearest whole percent.)<\/p>\n<\/li>\n A barangay\u2019s population increased from 8,000 to 9,200 in one year. What is the percentage increase?<\/p>\n<\/li>\n A jacket costing \u20b13,600 is discounted by 18%. What is the sale price?<\/p>\n<\/li>\n A grocery bill is \u20b12,450. If a customer gets a 10% discount coupon, how much does he pay after the discount?<\/p>\n<\/li>\n A machine\u2019s value depreciated from \u20b150,000 to \u20b137,500. What is the percentage decrease?<\/p>\n<\/li>\n After receiving a 25% discount, a customer pays \u20b12,250 for a certain item. What was the original price?<\/p>\n<\/li>\n A store offers successive discounts of 15% and 10% on a laptop with a tagged price of \u20b140,000. What is the final selling price?<\/p>\n<\/li>\n An employee\u2019s monthly salary is increased from \u20b122,000 to \u20b125,300. What is the percentage increase? (Round to the nearest tenth of a percent.)<\/p>\n<\/li>\n A water bill increased by 12% to \u20b11,568. What was the original bill before the increase?<\/p>\n<\/li>\n A cellphone originally priced at \u20b118,000 is offered at 20% discount. Additionally, the customer uses a voucher for another 5% discount on the already discounted price. What is the final amount to be paid?<\/p>\n<\/li>\n<\/ol>\n Items 1\u201310 (Multiple Choice)<\/strong><\/p>\n C<\/p>\n<\/li>\n C<\/p>\n<\/li>\n C<\/p>\n<\/li>\n C<\/p>\n<\/li>\n C<\/p>\n<\/li>\n B<\/p>\n<\/li>\n B<\/p>\n<\/li>\n C<\/p>\n<\/li>\n C<\/p>\n<\/li>\n B<\/p>\n<\/li>\n<\/ol>\n Solutions \/ Final Answers for Items 11\u201320<\/strong><\/p>\n 36 \u00f7 45 = 0.8 = 80%<\/strong><\/p>\n Increase = 9,200 \u2212 8,000 = 1,200 18% of 3,600 = 0.18 \u00d7 3,600 = 648 10% of 2,450 = 245 Decrease = 50,000 \u2212 37,500 = 12,500 Let original price = x First discount 15%: Second discount 10% on 34,000: Increase = 25,300 \u2212 22,000 = 3,300 Let original bill = x First discount 20%: Second discount 5% on 14,400: Civil Service Exam Philippines: Complete Preparation and Passing Guide<\/a><\/p><\/blockquote>\n\n
Converting Between Fractions, Decimals, and Percentages<\/h2>\n
Converting Fractions to Percentages<\/h3>\n
Converting Decimals to Percentages<\/h3>\n
Converting Percentages to Decimals<\/h3>\n
Converting Percentages to Fractions<\/h3>\n
Finding the Percentage of a Number<\/h2>\n
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\nWhat is 25% of 300?<\/p>\n
\n0.25 \u00d7 300 = 75<\/strong><\/p>\nPercentage Increase and Percentage Decrease<\/h2>\n
Percentage Increase Formula<\/h3>\n
Percentage Decrease Formula<\/h3>\n
\nA price increases from \u20b1200 to \u20b1260. What is the percentage increase?<\/p>\n
\nA price drops from \u20b1500 to \u20b1400. What is the percentage decrease?<\/p>\nUnderstanding Discounts<\/h2>\n
Discount Formulas<\/h3>\n
\nA bag originally costs \u20b11,200 and is discounted by 15%. What is the sale price?<\/p>\n
\n15% of 1,200 = 0.15 \u00d7 1,200 = 180<\/p>\n
\n1,200 \u2212 180 = \u20b11,020<\/strong><\/p>\nSuccessive Discounts<\/h2>\n
\nA jacket costs \u20b12,000 with successive discounts of 20% and 10%.<\/p>\n
\n20% of 2,000 = 400 \u2192 new price = 2,000 \u2212 400 = 1,600<\/p>\n
\n10% of 1,600 = 160 \u2192 final price = 1,600 \u2212 160 = \u20b11,440<\/strong><\/p>\nFinding the Original Price Before Discount<\/h2>\n
\nA shirt sells for \u20b1720 after a 20% discount. What was the original price?<\/p>\n
\nOriginal price = \u20b1900<\/strong><\/p>\nDiscount Rate When You Know Original Price and Sale Price<\/h2>\n
\nOriginal Price: \u20b11,500
\nSale Price: \u20b11,200<\/p>\n
\nDiscount Rate = (300 \u00f7 1,500) \u00d7 100 = 20%<\/strong><\/p>\nReal-Life Applications on the Civil Service Exam<\/h2>\n
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Useful Shortcuts for Exam<\/h2>\n
1. 10% is easy<\/h3>\n
\nExample: 10% of 450 is 45.<\/p>\n2. 5% is half of 10%<\/h3>\n
3. 1% is the number divided by 100<\/h3>\n
4. Combine shortcuts<\/h3>\n
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Common Mistakes to Avoid<\/h2>\n
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\nWrong: 20% + 10% = 30%
\nCorrect: Apply one discount after another.<\/li>\n
\nRemember that 20% is 0.20, not 20.<\/li>\n
\nThe second discount must use the discounted price<\/em>.<\/li>\nPractice Examples with Solutions<\/h2>\n
Example 1<\/h3>\n
\n0.12 \u00d7 850 = 102<\/strong><\/p>\nExample 2<\/h3>\n
\nRate = (180 \u00f7 900) \u00d7 100 = 20%<\/strong><\/p>\nExample 3<\/h3>\n
\nSale Price = 35,000 \u2212 6,300 = \u20b128,700<\/strong><\/p>\nExample 4<\/h3>\n
Example 5<\/h3>\n
\n30% of 5,000 = 1,500 \u2192 new price = 5,000 \u2212 1,500 = 3,500<\/p>\n
\n20% of 3,500 = 700 \u2192 final price = 3,500 \u2212 700 = \u20b12,800<\/strong><\/p>\nWhy This Topic Matters in the Civil Service Exam<\/h2>\n
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Tips for Answering Percentage Questions Faster<\/h2>\n
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Problem Sets<\/h2>\n
Set: Percentages and Discounts \u2013 Civil Service Exam Practice<\/h3>\n
Choose the correct answer for Items 1\u201310. For Items 11\u201320, write the final numerical answer only (no need to show solution in the exam, but practice showing it while reviewing).<\/p>\n
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A. 35
B. 40
C. 45
D. 50<\/p>\n<\/li>\n
A. 50
B. 55
C. 60
D. 65<\/p>\n<\/li>\n
A. 10%
B. 15%
C. 20%
D. 25%<\/p>\n<\/li>\n
A. 20%
B. 22%
C. 25%
D. 30%<\/p>\n<\/li>\n
A. 20%
B. 22.5%
C. 25%
D. 30%<\/p>\n<\/li>\n
A. \u20b1750
B. \u20b1765
C. \u20b1780
D. \u20b1800<\/p>\n<\/li>\n
A. \u20b11,750
B. \u20b11,800
C. \u20b11,900
D. \u20b12,000<\/p>\n<\/li>\n
A. \u20b12,250
B. \u20b12,400
C. \u20b12,500
D. \u20b12,800<\/p>\n<\/li>\n
A. 20%
B. 22.5%
C. 25%
D. 30%<\/p>\n<\/li>\n
A. \u20b1350
B. \u20b1375
C. \u20b1400
D. \u20b1425<\/p>\n<\/li>\n<\/ol>\n
\n\n
\nAnswer Keys<\/h2>\n
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\n\n
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1,200 \u00f7 8,000 \u00d7 100 = 15%
15%<\/strong><\/p>\n\n
3,600 \u2212 648 = \u20b12,952<\/strong><\/p>\n\n
2,450 \u2212 245 = \u20b12,205<\/strong><\/p>\n\n
12,500 \u00f7 50,000 \u00d7 100 = 25%
25%<\/strong><\/p>\n\n
After 25% discount: 0.75x = 2,250
x = 2,250 \u00f7 0.75 = \u20b13,000<\/strong><\/p>\n\n
15% of 40,000 = 6,000 \u2192 new price = 40,000 \u2212 6,000 = 34,000<\/p>\n
10% of 34,000 = 3,400 \u2192 final price = 34,000 \u2212 3,400 = \u20b130,600<\/strong><\/p>\n\n
3,300 \u00f7 22,000 \u00d7 100 \u2248 15.0%
15.0% (approx.)<\/strong><\/p>\n\n
12% increase \u2192 1.12x = 1,568
x = 1,568 \u00f7 1.12 = \u20b11,400<\/strong><\/p>\n\n
20% of 18,000 = 3,600 \u2192 new price = 18,000 \u2212 3,600 = 14,400<\/p>\n
5% of 14,400 = 720 \u2192 final price = 14,400 \u2212 720 = \u20b113,680<\/strong><\/p>\n
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