Why is a price lower after a 25% rise then a 25% fall?

The two percentages use different bases: the rise is taken on the original price, while the fall is taken on the larger raised price, so more is taken away than was added.

Should the original price be found by multiplying or dividing?

Divide. After a 25% rise the price is 125% of the original, so original = current × 100 ÷ 125.

Primary 6 Maths: Percentage Applications — Practice Paper 1 (10 Questions)

2026-10-29

Tutor Prep Guide · Primary Maths

Paper 1 runs from taking a percentage of a quantity through increases and decreases to discounts and reverse questions: part of a number first, then a rise and a fall, then the original price back from a sale price, the discount amount, and finally the error of rising then falling and expecting the same price.

Quick answer　Ten questions, about 20 minutes. Items 01 to 03 take a percentage, increase and decrease; items 04 to 06 cover a discount, a share of a group and a percentage rise; items 07 to 09 find the original price back from a raised or discounted price and the discount amount; item 10 redoes the rise-then-fall error.

01　Paper details (check answers afterwards)

Item	Detail
Questions	10 questions
Suggested time	20 minutes
Difficulty mix	Foundation 3 · Intermediate 3 · Challenge 3 · Error redo 1
Chapter	Chapter: Primary 6 Maths: Percentage Applications — Tutor Lesson Plan
Level	Primary 6

02　Questions (10 items)

FoundationWhat is 25% of 60?
FoundationIncrease 240 by 20%. What is the result?
FoundationDecrease 500 by 40%. What is the result?
IntermediateA item costs $320 and is sold at 20% off. What is the selling price?
IntermediateA class of 40 is 60% girls. How many girls and how many boys?
IntermediateAn item costs $80 and sells for $100. What is the percentage rise over cost?
ChallengeAfter a 25% rise an item sells for $250. What was the original price?
ChallengeAfter 20% off an item sells for $288. What was the original price?
ChallengeA book is sold at 20% off and $240 is paid. How much is the discount?
Error redoAn item at $100 rises 25% and then falls 25%. Is the price still $100? By how much does it differ?

03　Answers and one-line notes

#	Answer	One-line note
1	15	A percentage is “out of a hundred”: 25% = 25/100, so 60 × 25 ÷ 100 = 15.
2	288	A 20% increase means 120% of the original: 240 × 120 ÷ 100 = 288.
3	300	A 40% decrease leaves 60%: 500 × 60 ÷ 100 = 300.
4	$256	Twenty per cent off means paying 80%: 320 × 80 ÷ 100 = 256.
5	24 girls and 16 boys	40 × 60 ÷ 100 = 24 girls, and 40 − 24 = 16 boys.
6	25%	The rise is 100 − 80 = 20; dividing by the cost 80 gives 0.25, which is 25%.
7	$200	The new price is 125% of the original: 250 × 100 ÷ 125 = 200, and 200 × 1.25 = 250.
8	$360	The sale price is 80% of the original: 288 × 100 ÷ 80 = 360, and 360 × 0.8 = 288.
9	$60	The $240 paid is 80% of the original, so the original is 300 and the discount is 60.
10	No: it sells for $93.75, which is $6.25 below the original	100 × 1.25 = 125 and 125 × 0.75 = 93.75; the two percentages use different bases.

04　What to do after marking

After marking, redo only the wrong items and write down which step went wrong (formula, unit, or misread number).
Repeat the same item two days later; move to the next paper only when both attempts are correct.
Parents only need the answer and note columns; there is no need to explain every item.

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