This set has twelve original questions, ordered from easier to harder, covering all five lessons in percentages and changing bases. Questions 1 to 5 are warm-ups, 6 to 8 build reversing and comparing, and 9 to 12 mix skills.
Attempt each question on paper, without a calculator unless it says so, and write your working as you would in an exam. Only then open the answer. Mark the ones you got wrong and use the routing list at the end.
Questions
1. Find 30% of RM250.
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10% of 250 = 25. So 30% = 3 × 25 = RM75.
Check: 0.3 × 250 = 75. ✓
2. Find 17.5% of 240.
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10% = 24. 5% = 12. 2.5% = 6. Add: 24 + 12 + 6 = 42.
Check: 0.175 × 240 = 42. ✓
3. Write 18 as a percentage of 72.
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18 ÷ 72 = 1/4 = 0.25. As a percentage, 25%.
Check: 25% of 72 is 18. ✓
4. Jeans cost RM120. They are sold with 35% off. Find the sale price.
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10% of 120 = 12. 30% = 36. 5% = 6. So 35% = 36 + 6 = 42, and the discount is RM42. Sale price = 120 − 42 = RM78.
Check: paying 65% means 0.65 × 120 = 78. ✓
5. A parcel weighing 64 kg is increased in weight by 12.5%. Find the new weight.
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12.5% is one eighth. 64 ÷ 8 = 8. New weight = 64 + 8 = 72 kg.
Check: 64 × 1.125 = 72. ✓
6. After a 12% increase, a ticket costs RM168. Find the original price.
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Multiplier 1.12. Original = 168 ÷ 1.12 = RM150.
Check: 150 × 1.12 = 168. ✓
7. A coat is sold for RM204 after a 15% discount. Find the price before the discount.
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Multiplier 1 − 0.15 = 0.85. Original = 204 ÷ 0.85 = RM240.
Check: 240 × 0.85 = 204. ✓ The original must be greater than the sale price, and it is.
8. A bank raises its rate from 12% to 15%. Give the change in percentage points and the percentage increase in the rate.
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Points: 15 − 12 = 3 percentage points. Percentage increase: 3 ÷ 12 = 0.25, so 25%.
Check: 12 × 1.25 = 15. ✓
9. RM800 is increased by 10%, then the result is decreased by 10%. Find the final amount and the overall percentage change.
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800 × 1.1 = 880. Then 880 × 0.9 = RM792. Overall multiplier 1.1 × 0.9 = 0.99, which is a 1% decrease.
Check: 1% of 800 is 8, and 800 − 8 = 792. ✓ The amounts do not cancel because 10% of 880 is 88, not 80.
10. A price is increased by 25%, then decreased by 20%. Sara says the price returns to its start. Is she right? Explain.
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Multipliers: 1.25 × 0.8 = 1.00. So Sara is right.
Try 80 as the start: 80 × 1.25 = 100, then 100 × 0.8 = 80. ✓ The percentages are different (25% and 20%), so they cancel because each is taken from a different base. An equal rise and fall would not cancel.
11. A car worth RM60,000 loses 20% of its value each year. Find its value after 2 years.
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Multiplier 0.8 each year. After 2 years: 0.8² = 0.64. Value = 60000 × 0.64 = RM38,400.
Check by stages: 60000 × 0.8 = 48000, then 48000 × 0.8 = 38400. ✓ The loss is not 40% of 60000, which would leave 36000.
12. A population falls by 4% each year for 2 years and ends at 92,160. Find the starting population.
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Multiplier 0.96 each year. After 2 years: 0.96² = 0.9216. Original = 92160 ÷ 0.9216 = 100,000.
Check: 100000 × 0.96 = 96000, then 96000 × 0.96 = 92160. ✓
If you got these wrong
Match each error to a lesson, then retry a fresh question a few days later.
- Questions 1 to 5 (percentage of an amount, or finding a percentage by blocks): revisit find a percentage of an amount without a calculator.
- Questions 6, 7 and 12 (working back to the original): revisit reverse a percentage increase.
- Question 8 (rates, points and percent): revisit compare percentage change with percentage-point change.
- Questions 9, 10, 11 and 12 (stacked changes): revisit apply successive increases and decreases.
- Questions 9 and 10 (explaining why changes cancel or do not): revisit explain why equal percentage rise and fall do not cancel.
The percentage-base explorer can trace the amount at each stage, and the non-calculator working trainer supports the arithmetic. Record repeat errors in the mistake log and retest queue so the same type returns for a later retest.
Some students get the final numbers right but choose the wrong base on the next attempt. In online one-to-one Mathematics tuition, a teacher can read your working line by line and help you rebuild the step that keeps failing.