Choose the correct base and rate
Practise margins, mixtures and joint work.
The idea
Percentages must name their base. Rates add when independent workers act together; concentrations combine through the amounts of solute.
A method to try
- Write profit divided by the requested base.
- Convert each worker to jobs per hour.
- Add solute amounts before dividing by total volume.
Follow the reasoning.
A product costs 120 and sells for 150. Find profit as a percentage of cost and as a percentage of selling price.
- Profit is 150 − 120 = 30. Relative to cost, the percentage is 30/120 × 100 = 25%.
- Relative to selling price, it is 30/150 × 100 = 20%. Both calculations are valid, but they answer different questions.
- Before using a percentage, name its base in words. When a problem asks for a margin based on revenue, using cost as the denominator answers a different business question even though the arithmetic is correct.
Think it through first.
One worker completes a task in 4 hours and another in 12. Their combined rate is how many tasks per hour?
Show the explanation
1/3 task per hour.
Add 1/4 and 1/12, not the completion times. The combined completion time is then 3 hours.
Make it your own
After reading, explain the method in your own words and identify the condition that makes it valid. Then try the linked starter practice without referring back to the worked example. Review the reasoning behind an error before repeating the same item; remembering an answer is different from being able to solve a new problem.
This lesson is one part of a short starter pathway. It does not cover the full exam syllabus or establish a predicted score.
Official references
These provider and publisher links explain the exam or underlying concepts. Our lessons and questions are original, independent practice.
View 4 references and checked dates
- GMAC: exam structure (opens in a new tab)Checked 2026-10-06
- GMAC: exam content (opens in a new tab)Checked 2026-10-06
- GMAC: official preparation (opens in a new tab)Checked 2026-09-20
- GMAC: calculator and note-taking policies (opens in a new tab)Checked 2026-10-06