CORE_MATH • SHS 1Term 2WAEC / WASSCE SyllabusVIP Lesson
Ratio, Proportion, Rates of Work & Commercial Percentages
Sharing in ratios, direct and inverse proportion, rates of work (man-hours, water pipes), profit/loss, and discount.
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Real-World Context & Relevance in Ghana
Cocoa farming cooperatives in Sefwi Wiawso distribute end-of-year bonuses to member farmers proportionally based on the ratio of bags delivered.
Key Syllabus Learning Objectives
- 1Divide quantities into two or three-part ratios
- 2Solve rates of work and combined pipe filling problems
- 3Calculate percentage profit, loss, discount, and mark-up based on cost price
- 4Solve inverse proportion problems involving labor and completion time
1
Rates of Work Formula
Work problems rely on rate = work done / time. If Pipe A fills a tank in 4 hours and Pipe B fills it in 6 hours, their combined 1-hour rate is 1/4 + 1/6 = 5/12 of the tank. The tank fills in 12/5 = 2.4 hours.
- Find work done per single unit of time (1/t).
- Add rates for working together.
- Subtract rates if one empties while another fills.
- Invert the combined rate to find total time needed.
Core Takeaway:
Combined time is the reciprocal of the sum of individual hourly rates.
WAEC / WASSCE Examiner Tips
- Profit and loss percentage is ALWAYS calculated on the Cost Price unless the question specifically states otherwise.
- Ensure all quantities in a ratio are converted to the same unit before simplifying.
- State currency clearly in Ghana Cedis (GH₵).
Common Candidate Pitfalls & Errors to Avoid
- Calculating percentage profit using Selling Price as the denominator.
- Adding times directly in work problems instead of adding work rates.
- Confusing marked price with cost price.
Topic Mastery Checklist
- Can I divide GH₵ 24,000 in the ratio 3 : 5 : 4?
- Can I calculate the selling price of an item marked up by 25%?
- Can I calculate the time taken for two workers to complete a job together?
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