Name the base before you calculate each percentage. The eight questions use invented offers and rates, and follow the lessons in rates and percentages in multistep consumer questions.
For a timed run, use the timed original practice session builder.
Questions
Q1. A bag is sold at RM180 after a 25% discount. Find the original amount.
Answer
Multiplier = 0.75. Original = 180 ÷ 0.75 = RM240.
Check: 240 × 0.75 = 180.
Q2. A jacket is sold at RM144 after a 10% discount and then a further 20% off. Find the original amount.
Answer
Combined multiplier = 0.9 × 0.8 = 0.72. Original = 144 ÷ 0.72 = RM200.
Check: 200 × 0.9 = 180, and 180 × 0.8 = 144.
Q3. A quantity rises by 20% and then falls by 25%, ending at 270. Find the start.
Answer
Combined multiplier = 1.2 × 0.75 = 0.9. Start = 270 ÷ 0.9 = 300.
Check: 300 × 1.2 = 360, and 360 × 0.75 = 270.
Q4. A rate rises from 4% to 5%. State the change in percentage points and the percentage change.
Answer
Points: 5 − 4 = 1 point. Percentage change: 1 ÷ 4 × 100 = 25%.
Q5. A rate falls from 9% to 6%. State both changes.
Answer
Points: 6 − 9 = −3 points. Percentage change: −3 ÷ 9 × 100 = −33.3%.
Q6. A printer is sold for RM1 500 in cash. Plan 1 is 6 payments of RM265 and an RM20 processing fee.
Plan 2 is 12 payments of RM135. Which has the smaller total, and by how much?
Answer
Plan 1: 6 × 265 + 20 = RM1 610. Plan 2: 12 × 135 = RM1 620.
Plan 1 is smaller by RM10. Plan 2 has the smaller monthly payment but the larger total.
Q7. Item R is marked at RM150 with 40% off. Item S is marked at RM110 with 20% off. Which leaves the smaller amount to pay?
Answer
Item R: 150 × 0.6 = RM90. Item S: 110 × 0.8 = RM88.
Item S is RM2 smaller, despite the smaller discount.
Q8. Explain why a 30% discount followed by a 10% discount is not a 40% discount. Show the amounts for an item marked at RM400.
Answer
The 10% is taken from the reduced amount. Combined multiplier = 0.7 × 0.9 = 0.63, so the reduction is 37%.
For RM400: 400 × 0.63 = RM252. A single 40% discount would give 400 × 0.6 = RM240, which is RM12 less.
If you got these wrong
Reverse-calculation slips (Q1 to Q3) go to recovering an original amount after successive changes. Rate slips (Q4, Q5) go to percentage points and percentage change.
Plan slips (Q6) go to comparing instalment totals. Discount slips (Q7, Q8) go to why a bigger discount can cost more.
If you want a teacher to go through your working, see online one-to-one Mathematics tuition.