Why can successive discounts not be added?

The second discount applies to the reduced price, so the rates multiply: 20% then 10% off leaves 72%.

What do I divide by to work back to cost?

Divide by 1.15 for a 15% profit, or by 0.9 for a 10% loss.

Does one profit and one loss always cancel out?

No. Each percentage uses its own cost as the denominator, so add the amounts before comparing.

P6 Maths Discount, Profit and Loss Paper 2: Intermediate

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 is marked at 680 dollars and sold at 15% off. Find the selling price.
FoundationAn item costs 320 dollars. What selling price gives a profit of 15%?
FoundationAn item costing 250 dollars is sold for 300 dollars. Find the profit percentage.
IntermediateAn item is sold for 414 dollars at a profit of 15%. Find its cost.
IntermediateAn item is sold for 252 dollars at a loss of 10%. Find its cost.
IntermediateAn item marked at 800 dollars is sold for 680 dollars. Find the percentage discount.
ChallengeAn item marked at 450 dollars is discounted by 30% and then by a further 10%. Find the final price.
ChallengeAn item costs 480 dollars. The shop wants a 25% profit while selling at 20% off. What marked price is needed?
ChallengeTwo items cost 200 dollars and 300 dollars, and both are sold for 240 dollars. Find the overall profit or loss.
Error redoError review: a pupil says taking 20% off and then 10% off amounts to 30% off. What is the correct total discount?

03　Answers and one-line notes

#	Answer	One-line note
1	578 dollars	680 × 0.85 = 578 dollars.
2	368 dollars	320 × 1.15 = 368 dollars.
3	20%	(300 − 250) ÷ 250 × 100% = 20%.
4	360 dollars	Cost = 414 ÷ 1.15 = 360 dollars.
5	280 dollars	Cost = 252 ÷ 0.9 = 280 dollars.
6	15%	(800 − 680) ÷ 800 × 100% = 15%.
7	283.5 dollars	450 × 0.7 × 0.9 = 283.5 dollars; successive discounts multiply, they do not add.
8	750 dollars	The target selling price is 480 × 1.25 = 600 dollars, so the marked price is 600 ÷ 0.8 = 750 dollars.
9	a loss of 20 dollars	The takings are 480 dollars against a cost of 500 dollars, so the overall loss is 20 dollars.
10	28% (the price is 72% of the marked price)	0.8 × 0.9 = 0.72, so the price is 72% of the marked price and the total discount is 28%, not 30%.

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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