N3: PERCENTAGE COMMON QUESTIONS by @booksbfrboys on TikTok

N3: Percentage (Common Questions w/ Real-World Applications) - Expressing one quantity as percentage of another - Reverse percentages 1. In a particular school, the enrolment in 2016 is 900 students. In 2015, there were 20 more students than in 2016. There were 20 less students in 2016 % % as compared to 2017. Calculate the enrolment in (a) 2015 [1] (b) 2017 [1] 2. A shopkeeper bought a pair of shoes for $56. He still made a percentage profit of 15 even though he offered a 20 discount to his customer. % % Calculate the normal selling price of this pair of shoes. [2] 3. (a) Of the 195 countries in the world, Ryan has visited 20. What percentage of the countries in the world has Ryan visited? [1] 3. (b) At a sale, all prices are reduced by 22.5 . The price of a set of waterproof % headphones during the scale is $139.50. Find its original price. [1] 4. Express as a 8 3 4 % (a) decimal [1] (b) fraction in its simplest form [1] 5. The hire-purchase price of the refrigerator is 116 of the cash price. % The hire-purchase price is a deposit of 12 of the cash price plus 24 % monthly payments of $195. Find the cash price of the refrigerator. [3] 6. Paul sold a painting for $15680. He made a profit of 12 on the sale. % How much did he pay for the painting? [1]

7. The cash price of a sofa set is $8600. Caroline decided to pay by hire purchase with the following terms: ● A deposit of $500 and the balance amount of monthly instalments over a period of 3 years at a simple interest at 2.5 per annum. % Calculate the monthly instalments that Caroline has to pay. [3] 8. Bacteria in a petri dish multiply at a rate of 9.5 per hour. % At 1 pm, the population of bacteria in the petri dish was 3800. Find the population of bacteria at 2 pm. [2] 9. The marked price of a watch is $8000. If the watch is sold at the marked price, the retailer gains a profit of 60 . % Find the retailer’s profit if he sells it at a discount of 20 of the marked price. % [2] 10. A group of students sat for an examination. 50 of the boys and 40 of the girls passed the examination. % % Megan commented that 45 of the students passed the examination. % Explain why Megan may be wrong. [1]

N3: Percentage (Marking Scheme) 1. In a particular school, the enrolment in 2016 is 900 students. In 2015, there were 20 more students than in 2016. There were 20 less students in 2016 % % as compared to 2017. Calculate the enrolment in (a) 2015 2016 → 900 students 2015 → students 900 100 × 120%2015 → 1080 students 1080 students ∴ [1] (b) 2017 2016 → 900 students 2017 → students 900 80 × 100%2017 → 1125 students 1125 students ∴ [1] 2. A shopkeeper bought a pair of shoes for $56. He still made a percentage profit of 15 even though he offered a 20 discount to his customer. % % Calculate the normal selling price of this pair of shoes. Let the normal selling price be N Discounted price = N 0.20 N = 0.80 N −Shopkeeper made a 15 profit on cost price = = 64.40 % 56 100 × 115%Discounted price = 0.80 N = 64.40 N = = 80.50 64 . 40 80 × 100% $80.50 ∴ [2] 3. (a) Of the 195 countries in the world, Ryan has visited 20. What percentage of the countries in the world has Ryan visited? 20 195 × 100% = 10 . 256Percentage = 10.3 (3 s.f.) % ∴ 10 . 3% [1] 3. (b) At a sale, all prices are reduced by 22.5 . The price of a set of waterproof % headphones during the scale is $139.50. Find its original price. 139 . 50 77 . 5 × 100% = 180$180 ∴ [1]

4. Express as a 8 3 4 % (a) decimal 8 3 4 100 = 0 . 0875 ∴ 0 . 0875 [1] (b) fraction in its simplest form 8 3 4 100 = 7 80 ∴ 7 80 [1] 5. The hire-purchase price of the refrigerator is 116 of the cash price. % The hire-purchase price is a deposit of 12 of the cash price plus 24 % monthly payments of $195. Find the cash price of the refrigerator. 116 = 12 + 24 monthly payments of $195 % %116 % − 12% = 4680 104% = 4680 100% = 4500 ∴ $4500 [3] 6. Paul sold a painting for $15680. He made a profit of 12 on the sale. % How much did he pay for the painting? 15680 112 × 100% = 14 000 ∴ $14 000 [1] 7. The cash price of a sofa set is $8600. Caroline decided to pay by hire purchase with the following terms: ● A deposit of $500 and the balance amount of monthly instalments over a period of 3 years at a simple interest at 2.5 per annum. % Calculate the monthly instalments that Caroline has to pay. Balance after deposit = 8600 500 −Balance after deposit = 8100 Interest → 8100 ( 2 . 5 ) ( 3 ) 100 = 607 . 5Total amount to be paid (Balance + Interest) → 8100 + 607 . 5 = 8707 . 5Monthly instalment over 3 years (36 months) = 8707 . 5 36 Monthly instalment over 3 years (36 months) = 241.875 Monthly instalment over 3 years (36 months) = 241.88 (nearest cent) ∴ $241 . 88 [3]

8. Bacteria in a petri dish multiply at a rate of 9.5 per hour. % At 1 pm, the population of bacteria in the petri dish was 3800. Find the population of bacteria at 2 pm. 3800 100 × 109 . 5 = 4161 ∴ 4161 [2] 9. The marked price of a watch is $8000. If the watch is sold at the marked price, the retailer gains a profit of 60 . % Find the retailer’s profit if he sells it at a discount of 20 of the marked price. %Profit = selling price cost price −Since profit is 60 , selling price is 160 (100 + 60 profit) % % % %Cost price = 8000 160 × 100% = 5000Discounted selling price = 8000 100 × 80% = 6400Profit = 6400 5000 −Profit = 1400 $1500 ∴NOTE: you do not need to say everything you’re doing, this marking scheme is to guide and help you understand the steps. [2] 10. A group of students sat for an examination. 50 of the boys and 40 of the girls passed the examination. % % Megan commented that 45 of the students passed the examination. % Explain why Megan may be wrong. The number of boys and girls in the school may not be equal. ∴ [1]