Word Problems Made Simple: A Four-Step Method for the CSE

Word problems are the third item in the official Numerical Ability scope of the Civil Service Exam, and many examinees fear them more than any other question type. Usually the arithmetic is simple. The difficulty is turning words into a calculation. This guide gives you a four-step method and shows it working on the problem types that appear most often.

The four steps

1. Understand: read the problem twice. Underline what is given and circle what is asked.
2. Translate: turn the words into numbers and a simple equation or calculation.
3. Solve: do the arithmetic carefully, by hand.
4. Check: put your answer back into the story. Does it make sense?

Most mistakes happen in step 1 (answering a different question from the one asked) or are caught in step 4.

Key words and what they mean

Words	Operation
total, sum, combined, more than	addition
difference, less than, left, remaining	subtraction
of, times, product, per (for rate × quantity)	multiplication
per, each, ratio, average, divided equally	division
percent	÷ 100

“Of” is especially important: “3/4 of 480” means 3/4 × 480.

Type 1: Percentages and discounts

A shirt priced at ₱1,250 is sold at 20% off. What is the sale price?

• Translate: you pay 100% − 20% = 80% of the price.
• Solve: 80% of 1,250 = 0.8 × 1,250 = ₱1,000.
• Check: the discount, ₱250, is a fifth of ₱1,250. ✔

Trap: percentage change is always based on the original value. A price rising from ₱80 to ₱100 is a 25% increase (20 ÷ 80), not 20%.

Type 2: Ratio and sharing

₱36,000 is shared between Ana and Ben in the ratio 4 : 5. How much does Ben get?

• Translate: 4 + 5 = 9 equal parts.
• Solve: one part = 36,000 ÷ 9 = 4,000. Ben gets 5 × 4,000 = ₱20,000.
• Check: Ana gets 16,000; 16,000 + 20,000 = 36,000. ✔

Type 3: Work and time

Cris can finish a job in 6 days, and Dan in 12 days. How long do they take together?

• Translate: Cris does 1/6 of the job per day, Dan 1/12.
• Solve: together 1/6 + 1/12 = 2/12 + 1/12 = 3/12 = 1/4 per day, so 4 days.
• Check: the answer must be less than 6 days (Cris alone). ✔

Shortcut for two people: time together = (a × b) ÷ (a + b) = (6 × 12) ÷ 18 = 4.

Type 4: Speed, distance and time

Remember one triangle: distance = speed × time.

A bus travels 240 km at 60 km/h. How long does the trip take?

• Solve: time = distance ÷ speed = 240 ÷ 60 = 4 hours.

Trap: for average speed over a round trip at two different speeds, do not average the speeds. Divide total distance by total time.

Type 5: Simple interest

Interest = principal × rate × time

₱50,000 at 6% per year for 3 years → 50,000 × 0.06 × 3 = ₱9,000.

Type 6: Ages

A father is three times as old as his son. In 12 years he will be twice as old. How old is the son?

• Translate: let the son be x, the father 3x. In 12 years: 3x + 12 = 2(x + 12).
• Solve: 3x + 12 = 2x + 24, so x = 12.
• Check: now 12 and 36; in 12 years 24 and 48, and 48 is twice 24. ✔

Type 7: Proportion

If 5 kilos of rice cost ₱275, how much do 12 kilos cost?

Find the cost of one unit first: 275 ÷ 5 = ₱55, then 12 × 55 = ₱660.

For inverse proportion (more workers, fewer days), multiply first: 8 workers × 15 days = 120 worker-days; with 12 workers, 120 ÷ 12 = 10 days.

When you get stuck

• Work backwards from the options. Put each option into the story and see which one fits. This is often faster for age and coin problems.
• Use simpler numbers. Replace the numbers with easy ones to see the method, then go back to the real numbers.
• Draw it. A quick sketch of a timeline, a bar split into parts or a table often makes the relationships clear.

Practise the method, not just the answers

When you review, do not just note the right answer. Write down which type the problem was and which step went wrong. After a few weeks you will recognise the type of most problems as soon as you read them.

Work through our numerical word problems, then the data interpretation tables for Professional level practice. Every answer was calculated and checked by script, and each explanation follows the steps above.