Numerical Ability · Editorial

Word problems

Word problems reviewer for the CSE: age, work, distance, mixture, ratio, and percent problems with formulas, a step-by-step method, and practice items with answers.

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CSEPass editorial teamUpdated Facts checked How we source facts5 min readEditorial

Word problems are story-shaped Numerical Ability items: age, work, distance, mixture, profit, and ratio situations. On the CSE-PPT, the math is usually grade-school level; the hard part is translating the story into the right equation under time pressure.

Key takeaways

  • Word problems use grade-school math; the hard part is translating the story into an equation.
  • Learn the formula for each problem type: distance, work, age, ratio, percent, and mixture.
  • Define one variable for what you need, and check that your answer is what the question asked.
  • Plug in the choices when setting up an equation feels slow; one of them must work.

Formulas by problem type

TypeFormula or methodExample setup
Distancedistance = rate × time120 km at 60 km/h → 2 hours
Workcombined rate = 1/a + 1/b6 h and 3 h → 1/6 + 1/3 = 1/2 → 2 hours
Ageboth ages change by the same number of yearsIn 5 years: (x + 5) and (y + 5)
Ratioparts × (total ÷ sum of parts)₱900 in 2:3 → 900 ÷ 5 = 180 → ₱360 and ₱540
Percentpart = rate × base15% of ₱2,000 = ₱300
Mixtureamount × concentration is conserved10 L of 20% + 10 L of 40% → 30%
Consecutive numbersx, x + 1, x + 2 (odd or even: x, x + 2, x + 4)Three consecutive numbers sum to 48 → x = 15

How to approach

  1. Underline the ask. Know exactly what is requested (Ana’s share? time left? selling price?).
  2. Assign one variable. Prefer the unknown you need; avoid three variables for a one-unknown story.
  3. Translate phrases. *Twice as many* → ×2; *₱40 less* → −40; *split in ratio 2:3* → 2x and 3x.
  4. Draw a line for rates. Work and distance problems get easier with a tiny rate × time table.
  5. Sanity-check units. Hours vs. minutes, pesos vs. pieces, one-way vs. round trip.

Worked example

Stem: Liza and Mark paint a waiting shed. Liza alone finishes in 6 hours; Mark alone in 3 hours. How long do they take working together?

  1. A.1 hour
  2. B.2 hours
  3. C.2.5 hours
  4. D.4.5 hours

Work: Liza’s rate = 1/6 shed/hour; Mark’s = 1/3 = 2/6. Together = 3/6 = 1/2 shed/hour. Time = 1 ÷ (1/2) = 2 hours. Answer: B. 2 hours.

Common traps

  • Adding times instead of rates — Averaging 6 and 3 to get 4.5 (a common wrong option).
  • Ratio total slip — Using parts 2 and 3 but dividing the peso amount by 2 or 3 only.
  • Rest/discount double-count — Applying a tip or tax to the wrong base amount.
  • Age “years ago” errors — Forgetting both people age by the same number of years.
  • Leaving the variable — Solving for *x* when the question asked for *3x* (the larger share).

Quick practice

  1. A jeepney fare is ₱15 for the first 4 km and ₱2 per additional km. Cost for 9 km?
  1. A.₱23
  2. B.₱25
  3. C.₱27
  4. D.₱30

Answer: B — 15 + 2×(9−4) = 15+10 = 25.

  1. Ben has twice as many pens as Carla. Together they have 36. How many does Ben have?
  1. A.12
  2. B.18
  3. C.24
  4. D.30

Answer: C — B=2C; 2C+C=36 → C=12 → B=24.

  1. A bus travels 180 km at 45 km/h. How long is the trip?
  1. A.3 hours
  2. B.4 hours
  3. C.4.5 hours
  4. D.5 hours

Answer: B — time = 180 ÷ 45 = 4 hours.

  1. ₱1,200 is divided between Ana and Ben in the ratio 3:5. How much does Ben get?
  1. A.₱450
  2. B.₱600
  3. C.₱720
  4. D.₱750

Answer: D — 1,200 ÷ 8 = 150 per part; Ben gets 5 × 150 = ₱750.

  1. Rico is 4 times as old as his son. In 6 years, he will be 3 times as old. How old is the son now?
  1. A.8
  2. B.10
  3. C.12
  4. D.14

Answer: C — 4x + 6 = 3(x + 6) → 4x + 6 = 3x + 18 → x = 12.

  1. The sum of three consecutive even numbers is 78. What is the largest?
  1. A.24
  2. B.26
  3. C.28
  4. D.30

Answer: C — x + (x + 2) + (x + 4) = 78 → 3x = 72 → x = 24; largest = 28.

Frequently asked questions

What kinds of word problems are in the Civil Service Exam?

Common types are age, work, distance–rate–time, ratio and proportion, percent (discounts, interest, increases), mixtures, and consecutive numbers.

How do I solve word problems faster?

Underline what is asked, write one equation, and estimate. If the algebra is slow, test the answer choices in the story; one will fit.

Study with this product

  1. Take the free diagnostic to see if this topic is a weakness.
  2. Drill Word problems in Practice—this topic usually needs the most reps—or follow Today’s plan.
  3. Sit a full mock when recommended so translation speed survives exam fatigue.

Honest facts

  • This guide is a study aid, not an official CSC reviewer and not a pass promise.
  • We never invent official CSC dates, fees, or room assignments.
  • Sample stems here are original practice items for skill-building, not leaked exam content.
  • Readiness Score is a product metric — not a CSC rating prediction.

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