Does a mark-up followed by a discount always raise the price?

No. The two percentages multiply; a 25% rise and a 20% discount leave the original price.

For a profit after a discount, which step comes first?

Find the sale price needed from the cost, then divide by the discount factor to get the marked price.

P6 Maths Discount, Profit and Loss Paper 3: Challenge

2026-11-09

Tutor Prep Guide · P6 Maths

Ten original items, each with an answer and a one-line explanation.

Direct answers　Items 1-3 are basic, 4-6 intermediate and 7-9 challenge, with item 10 as the error review. Time yourself first, then check every answer and redo the wrong ones.

01　Paper details (check answers afterwards)

Item	Detail
Questions	10
Suggested time	20
Difficulty mix	Foundation 3 · Intermediate 3 · Challenge 3 · Error redo 1
Chapter	Chapter: P6 Maths Discount, Profit and Loss
Level	P6

02　Questions (10 items)

FoundationAn item marked at 1200 dollars gets 20% off and then a further 5% off. Find the final price.
FoundationAn item costing 450 dollars is sold for 540 dollars. Find the profit percentage.
FoundationThe same item costs 450 dollars. What price gives a 30% profit?
IntermediateAn item sells for 644 dollars at a profit of 15%. Find the cost.
IntermediateAn item costs 270 dollars. The shop wants an 8% profit while selling at 10% off. Find the marked price.
IntermediateAn item costs 500 dollars, is marked at 700 dollars and is finally sold at 40% off. Find the loss percentage.
ChallengeAn item marked at 960 dollars is raised by 25% and then sold at 20% off. Find the final price.
ChallengeTwo items cost 400 dollars and 600 dollars and both sell for 480 dollars. Find the overall result.
ChallengeAn item costs 320 dollars. The shop wants a 20% profit while selling at 20% off. Find the marked price.
Error redoError review: a pupil says a 200-dollar item marked up by 50% and then sold at 20% off gives 50% − 20% = 30% profit. What is the correct profit percentage?

03　Answers and one-line notes

#	Answer	One-line note
1	912 dollars	1200 × 0.8 × 0.95 = 912 dollars.
2	20%	(540 − 450) ÷ 450 × 100% = 20%.
3	585 dollars	450 × 1.3 = 585 dollars.
4	560 dollars	Cost = 644 ÷ 1.15 = 560 dollars.
5	324 dollars	The sale price must be 270 × 1.08 = 291.6 dollars, so the marked price is 291.6 ÷ 0.9 = 324 dollars.
6	16%	The price is 700 × 0.6 = 420 dollars, a loss of 80 dollars, so 80 ÷ 500 × 100% = 16%.
7	960 dollars	960 × 1.25 × 0.8 = 960 dollars, which is exactly the original marked price.
8	a loss of 40 dollars	Takings are 960 dollars against a cost of 1000 dollars, so the loss is 40 dollars.
9	480 dollars	The sale price must be 384 dollars, so the marked price is 384 ÷ 0.8 = 480 dollars.
10	20%	The marked price is 300 dollars and it sells for 240 dollars, a profit of 40, so 40 ÷ 200 × 100% = 20%.

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.

Book a Maths tutor Tutor Registration →

Questions and answers are written originally by the TutorZone team and are not taken from any school, publisher or examination authority paper. Every value is checked by computer.