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Math · Algebra

Age, work, and mixture word problems

Translate a real scenario — ages, work rates, or mixtures — into an equation, then solve it. The algebra is rarely hard; the setup is where marks disappear. Every question comes with a written breakdown of how the equation was built, not just how it was solved.

Practise age, work, and mixture word problems nowSee sample questions
3
Difficulty tiers
60s
Target pace
48%
Average first-attempt score

What's covered

  • Age problems — set up expressions for age at different points in time — now, x years from now, x years ago — and translate the sentence's condition into an equation.
  • Work-rate problems — combine rates as fractions of a job per unit time; the shared variable is time, not the individual rates themselves.
  • Mixture problems (concentration) — balance a substance's amount across two components using a weighted-average equation, not a simple average.
  • Mixture problems (cost per unit) — apply the same weighted-average structure to price and quantity instead of concentration.
  • Translating the language — convert phrases like more than, less than, and twice as into the correct operations and order — the single biggest source of setup errors.

Where students lose marks

Writing the relationship backwards

"5 years older than twice his age" and "twice 5 years older than his age" translate to different equations. Read the sentence right to left if the order isn't clicking.

Adding work rates as times instead of rates

Two workers finishing a job in 6 hours and 3 hours don't finish together in 9 hours, or in the average of the two — rates add, times don't. Convert to "job per hour" first.

Ignoring that a mixture equation needs volume AND concentration to balance

A mixture problem hides two conditions in one sentence — the total amount and the total concentration both have to check out, not just one of them.

Three sample questions

Straight from the bank — one per difficulty tier. Reveal the answer to see the explanation you'd get in a real session.

Sample 01Foundation

In 5 years, Raj will be twice as old as he was 3 years ago. How old is Raj now?

Sample 02Core

Pipe A can fill a tank in 6 hours. Pipe B can fill the same tank in 3 hours. Working together, how many hours will it take to fill the tank?

Sample 03Advanced

A chemist has 10 liters of a solution that is 20% acid. How many liters of pure acid must be added to make the mixture 50% acid?

How to practise this

Word problems are an algebra skill wearing a disguise — the setup is what's being tested, and that's exactly what untimed drilling builds before the clock gets added.

Write the equation before solving

For every problem, write out the full equation from the words alone before doing any algebra. Untimed practice is where you build that separation between setup and solving.

Then 60 seconds a question

Move to timed sessions once you can set up an equation without hesitating. Word problems run longer than pure algebra since there's a sentence to translate first.

Fold into a mock

Combine word problems with linear equations and quadratic equations in a mock — all three end in the same solving step, just with different setups.

Stop staring at the words.
Start writing the equation.

  • A written breakdown of the setup on every item — not just the solving steps
  • Timed or untimed sessions, any length you like
  • Tracked separately — see your accuracy and pace on word problems over time
Start practising free

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