Civil Service Math: Percentages, Ratios, and Word Problems Explained

Translate the sentence before calculating

Numerical ability is part of both Professional and Subprofessional coverage. The CSC scope includes basic operations, number sequences, and word problems. This lesson concentrates on a useful subset of those skills, rather than claiming that percentages or ratios have a fixed number of questions in the examination.

First, write the requested quantity: discount, final price, original amount, share, or rate. Next, identify the information you have and keep its units attached. Then write a short relationship before inserting numbers. Finally, estimate the size of the answer. A discount larger than the original price should make you stop and check your work.

Three relationships handle many basic exercises: percentage amount equals rate times base; percentage change equals change divided by original amount times 100; and one ratio part equals the total divided by the sum of the parts. These are tools to understand, not words that automatically select an operation. Read the whole situation before choosing one.

Eight original worked examples

1. Find a percentage of an amount

Problem: A supply budget is ₱1,200. What is 15% of that budget? Here, ₱1,200 is the whole and 15% is the requested share. Calculate 0.15 × 1,200 = ₱180. For a mental check, 10% is ₱120 and 5% is ₱60; together they are ₱180. The question asks for the share, not the money remaining.

2. Separate a discount from the final price

Problem: A bag costs ₱800 before a 25% discount. What is the sale price? The discount is one quarter of ₱800, or ₱200. Subtract it: 800 − 200 = ₱600. Alternatively, pay the remaining 75%: 0.75 × 800 = 600. Both methods agree. Answering ₱200 would correctly calculate a related quantity but miss the requested final price.

3. Recover an original amount

Problem: After a 20% discount, a desk costs ₱960. What was its original price? The sale price is 80% of the original, so 0.80 × original = 960. Divide: 960 ÷ 0.80 = ₱1,200. Check by removing ₱240 from ₱1,200. Adding 20% of ₱960 gives the wrong result because it uses the reduced price as the base.

4. Measure percentage increase

Problem: A team's weekly completed requests rise from 240 to 300. What is the percentage increase? The increase is 300 − 240 = 60 requests. Divide by the original 240: 60 ÷ 240 × 100 = 25%. Dividing by 300 would produce 20%, which answers a different comparison. Always identify which quantity represents the starting point.

5. Divide a total using a ratio

Problem: Two groups share 64 folders in the ratio 3:5. How many does each receive? There are 3 + 5 = 8 equal parts, so each part contains 64 ÷ 8 = 8 folders. The shares are 3 × 8 = 24 and 5 × 8 = 40 folders. They total 64 and simplify back to 3:5, giving two independent checks.

6. Distinguish part-to-part from part-to-whole

Problem: Blue pens and black pens are in the ratio 2:3. What percentage of all pens are blue? Blue pens account for two of the five total parts, so 2 ÷ 5 × 100 = 40%. The fraction 2/3 compares blue pens with black pens, not with all pens. Writing “blue / all” before substituting numbers prevents that mistake.

7. Apply a constant rate with matching units

Problem: A printer produces 18 pages per minute at a constant rate. How many minutes does it need for 270 pages? Time equals pages divided by pages per minute: 270 ÷ 18 = 15 minutes. Check with 18 × 15 = 270. This exercise assumes no interruptions and a constant rate; do not add waiting periods that the problem never mentions.

8. Build an equation for an unknown quantity

Problem: Four identical notebooks and a ₱35 pen cost ₱195 altogether. What does one notebook cost? Let the notebook price be n. Then 4n + 35 = 195. Remove the pen cost first: 4n = 160. Divide by four: n = ₱40. Substitute back: four notebooks cost ₱160, and the pen brings the total to ₱195.

Catch the error before choosing an answer

Percentages describe a relationship to a base. Two successive changes do not necessarily cancel: a ₱100 amount increased by 10% becomes ₱110; reducing that new amount by 10% gives ₱99. The second percentage acts on a different base. When a question involves multiple steps, label the amount after each step rather than combining percentages automatically.

Keep fractions exact until the last step where possible. For example, one third of 90 is exactly 30; rounding one third to 0.33 first produces 29.7. Also distinguish percentage points from percentage change. A rate moving from 20% to 25% rises by five percentage points, while its relative increase is 5 ÷ 20 = 25%.

• Check whether the question asks for the amount changed or the new total.
• Add ratio parts before dividing a shared total.
• Convert hours and minutes before combining rates and times.
• Use an estimate to reject answers with an implausible size.

Five questions to solve before reading the answers

These are original practice questions, not official examination items. Work them without a calculator to practise the operations. Write one line explaining your setup for each answer. An answer alone does not show whether you understood the relationship or happened to select the right operation.

1. A group has 350 participants. If 18% attend a morning workshop, how many attend that workshop?
2. A chair costs ₱1,020 after a 15% discount. What was its original price?
3. Two offices divide 84 envelopes in the ratio 2:5. How many envelopes does each office receive?
4. A monthly count falls from 500 to 425. What is the percentage decrease?
5. Three identical notebooks and two pens costing ₱18 each cost ₱171 altogether. What is the price of one notebook?

Answers and explanations

1. 63 participants

Find 18% of the full 350: 0.18 × 350 = 63. A second method is 20% minus 2%: 70 − 7 = 63. The result is a count of participants, not a percentage. Subtracting from 350 would instead tell you how many did not attend.

2. ₱1,200

The chair retains 85% of its original price. Divide 1,020 by 0.85 to obtain 1,200. Verify that 15% of 1,200 is 180 and 1,200 − 180 = 1,020. Using 15% of the discounted amount would apply the rate to the wrong base.

3. 24 and 60 envelopes

The seven ratio parts represent all 84 envelopes. Each part is 12, so the first office gets 2 × 12 = 24 and the second gets 5 × 12 = 60. Check both the total, 84, and the simplified ratio, 2:5.

4. 15%

The decrease is 500 − 425 = 75. Compare it with the original 500: 75 ÷ 500 × 100 = 15%. The remaining count is 85% of the original. Reporting 85% would describe the amount retained rather than the decrease requested.

5. ₱45

The two pens cost 2 × 18 = 36 pesos. That leaves 171 − 36 = 135 pesos for three notebooks, so each costs 135 ÷ 3 = 45 pesos. Substitution confirms the total: 3 × 45 + 2 × 18 = 171.

Repeat the method with fresh numbers

Mark each missed answer as a reading, setup, calculation, or unit error. Rework it tomorrow without viewing the solution, then solve a fresh question of the same type. Add timed practice only after you can explain the method. Your next target is a reliable sequence of decisions, not memorising the numbers on this page.