A stationery shop owner made ₹8000 selling books, of which 30% is the profit amount, and ₹1000 selling book covers, of which 50% is the profit amount. What is the percentage of profit on the total sales?
Step-by-step solution
To find: Profit as a percentage of the total sales
Idea: The profit percentages are like concentrations, and the sales amounts are the quantities. The overall percentage is their weighted mean, so it will be much nearer 30% than 50%.
- Profit on books = 30% of ₹8000 = ₹2400; profit on covers = 50% of ₹1000 = ₹500. Total profit = ₹2900.1 mark
- Total sales = ₹8000 + ₹1000 = ₹9000. Profit % = 29009000 × 100 = 32.22…% ≈ 32.22%.1 mark
Check: Weighted mean 30 × 8000 + 50 × 10009000 = 2900009000 ≈ 32.22 ✓. It is close to 30% because books make up most of the sales ✓.
Answer to write in the exam
Profit = 30100 × 8000 + 50100 × 1000 = 2400 + 500 = ₹2900
Total sales = 8000 + 1000 = ₹9000
Profit % = 29009000 × 100 = 32.22%
∴ Percentage of profit on total sales ≈ 32.22%
Common mistakes that cost marks
- Averaging 30% and 50% to get 40%. The book sales are 8 times the cover sales, so 30% must count much more.
- Adding 30% and 50% to get 80%.
- Dividing the profit by ₹8000 only, instead of the total sales ₹9000.
How this can come in the exam
A shop sells ₹6000 of goods at 20% profit and ₹4000 of goods at 10% profit (profit as a percentage of sales). The overall profit percentage is
- 15%
- 16%
- 14%
- 30%
Show answer
(B) 16%
1200 + 40010000 × 100 = 16%.
Try one yourself
A trader’s sales are ₹5000 at 40% profit and ₹15000 at 20% profit (profit as a percentage of sales). Find the overall profit percentage.
Show answer
Profit = 2000 + 3000 = ₹5000 on sales of ₹20000, so 500020000 × 100 = 25%.
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