Grade 10 essential mathematics – Commercial Arithmetic I Quiz
1. A businessman borrows Ksh 60,000 at a simple interest rate of 8% per annum for 3 years. What is the simple interest due?
Simple interest = P × R × T / 100 = 60,000 × 8 × 3 / 100 = 14,400 Ksh.
2. If Ksh 8,000 is invested at 5% simple interest per annum, how much total amount will there be after 4 years?
Simple interest = 8,000 × 5 × 4 / 100 = 1,600. Total amount = 8,000 + 1,600 = 9,600 Ksh.
3. A shopkeeper buys goods for Ksh 15,000 and sells them for Ksh 18,000. What is his profit percentage?
Profit = 18,000 − 15,000 = 3,000. Profit % = (3,000 / 15,000) × 100 = 20%.
4. An item is marked at Ksh 5,000. The shop offers a 10% discount. What is the selling price after the discount?
Discount = 10% of 5,000 = 500. Selling price = 5,000 − 500 = 4,500 Ksh.
5. A trader marks up the cost price by 25%. If the cost price is Ksh 2,400, what is the marked price?
Markup = 25% of 2,400 = 600. Marked price = 2,400 + 600 = 3,000 Ksh.
6. A lender charges simple interest and receives Ksh 1,125 interest on a loan of Ksh 5,000 over 3 years. What is the annual rate (%)?
Rate R = (SI × 100) / (P × T) = (1,125 × 100) / (5,000 × 3) = 112,500 / 15,000 = 7.5%.
7. A retailer sells an article at a loss of 12%. If the selling price is Ksh 6,600, what was the cost price?
Let CP = x. SP = x(1 − 0.12) = 0.88x = 6,600 → x = 6,600 / 0.88 = 7,500 Ksh.
8. A wholesaler gives a trade discount of 15% on Ksh 20,000 order. How much does the buyer pay?
Discount = 15% of 20,000 = 3,000. Amount payable = 20,000 − 3,000 = 17,000 Ksh.
9. A trader declares a 12% profit on cost. If his cost is Ksh 25,000, what is the selling price?
Profit = 12% of 25,000 = 3,000. Selling price = 25,000 + 3,000 = 28,000 Ksh.
10. If a merchant reduces the price of an item by 20% and then applies another 10% discount on the reduced price, the overall discount is:
Overall multiplier = 0.8 × 0.9 = 0.72 so overall discount = 1 − 0.72 = 0.28 = 28%.
11. A loan of Ksh 4,500 attracts simple interest at 6% per annum. What is the interest for 2 years 6 months?
Time = 2.5 years. Interest = 4,500 × 6 × 2.5 / 100 = 675 Ksh.
12. A trader bought goods for Ksh 9,200 and sold them at a 15% profit. He then gave a customer a 10% discount on the selling price. What is the final price paid by the customer?
Marked selling price = 9,200 × 1.15 = 10,580. After 10% discount: 10,580 × 0.9 = 9,522. Wait recalculation: 10,580 × 0.9 = 9,522. Correction: choose correct option. (Note: correct final price is Ksh 9,522.)
13. A cashier computes a 5% commission on sales. If sales amount to Ksh 48,000, how much is the commission?
Commission = 5% of 48,000 = 0.05 × 48,000 = 2,400 Ksh.
14. A merchant sold goods for Ksh 7,350 with a gain of 10%. What was the cost price?
Let CP = x, SP = x × 1.10 = 7,350 → x = 7,350 / 1.10 = 6,681.818..., rounded to Ksh 6,681.82.
15. If a commodity's price increases by 12% and later decreases by 10%, the net percentage change is approximately:
Net multiplier = 1.12 × 0.90 = 1.008 → net change = 0.8%? Wait compute: 1.12×0.9=1.008 so 0.8% increase. Correct is 0.8% increase. (Note: corrected net change is 0.8% increase.)
16. A customer buys goods worth Ksh 2,500. VAT at 16% is added. What is the total amount to be paid?
VAT = 16% of 2,500 = 400. Total = 2,500 + 400 = 2,900 Ksh.
17. A shopkeeper wants a 25% profit on selling price. If the cost price is Ksh 3,600, what selling price should he set? (Profit on selling price means profit = 25% of SP.)
Let SP = s. Profit = 0.25s and CP = s − 0.25s = 0.75s = 3,600 → s = 3,600 / 0.75 = 4,800 Ksh.
18. A trader pays Ksh 2,400 for goods and sells them at Ksh 3,120. What is the profit percent?
Profit = 3,120 − 2,400 = 720. Profit % = (720 / 2,400) × 100 = 30%.
19. A borrower repays Ksh 2,600 after 3 years on a loan of Ksh 2,000. What was the simple interest rate per annum?
Interest = 2,600 − 2,000 = 600. Rate = (600 × 100) / (2,000 × 3) = 60,000 / 6,000 = 10%.
20. An item costs Ksh 1,800 including a 20% profit on cost. What was the original cost price?
If CP = x, SP = x × 1.20 = 1,800 → x = 1,800 / 1.20 = 1,500 Ksh.
21. A wholesaler sells an article at Ksh 4,400 after allowing two successive discounts of 10% and 5% on the marked price. What was the marked price?
Overall multiplier = 0.90 × 0.95 = 0.855. Marked price = 4,400 / 0.855 ≈ 5,440 Ksh.
22. A salesman gets a commission of 3% on all sales. If his commission in a month was Ksh 3,600, what value of goods did he sell?
If sales = S, commission = 0.03S = 3,600 → S = 3,600 / 0.03 = 120,000 Ksh.
23. A trader offers 12.5% discount on a marked price. If the selling price after discount is Ksh 1,750, what was the marked price?
Selling price = 0.875 × marked price. Marked price = 1,750 / 0.875 = 2,000 Ksh.
24. An article sold at Ksh 2,160 gives a loss of 10%. What should be the selling price to make a 20% profit on the cost price?
If CP = x and SP at 10% loss = 0.90x = 2,160 → x = 2,400. For 20% profit SP = 1.20 × 2,400 = 2,880 Ksh.
25. A bank discounts a bill of exchange of face value Ksh 50,000 for 4 months at a simple discount rate of 9% per annum. What is the banker's discount?
Banker's discount = Face value × rate × time = 50,000 × 9% × (4/12) = 50,000 × 0.09 × 1/3 = 1,500 Ksh.