Work through the levels in order. Type your answer and press Check — open the worked solution if you get stuck. Answers like -6, 3/4 or 0.25 are typed exactly as shown. A ⭐ Bonus Challenge at the end is extra credit — skip it if the rest was hard work.
Level 1 · Warm-up
1 A phone plan costs $45 a month. The price rises by 4%. What is the new cost for a whole year?
Show worked solution
45 × 1.04 = $46.80 a month. 46.80 × 12 = $561.60. ($540 is the old yearly cost; $21.60 is only the extra; $588 adds $4 a month instead of 4%.)
2 Concert tickets went from $56 to $63. Find the increase in dollars and the percentage increase.
Show worked solution
Increase: 63 − 56 = $7. 7 ÷ 56 = 0.125 = 12.5%.
3 A school’s enrolment fell by 4% to 912 students. How many students were enrolled before the fall?
Show worked solution
Old × 0.96 = 912, so old = 912 ÷ 0.96 = 950 students. Check: 4% of 950 is 38, and 950 − 38 = 912.
Level 2 · Core
4 A painting was sold for $5400, making a 35% profit on what the owner paid for it. What did the owner pay?
Show worked solution
Cost × 1.35 = 5400, so cost = 5400 ÷ 1.35 = $4000. ($3510 takes 35% off the selling price — the reverse trap; $1890 is 35% of $5400; $7290 adds 35% again.)
5 A flat’s weekly rent changed over two years as shown. Find the percentage increase in each year.
Show worked solution
Year 1: 40 ÷ 500 = 0.08 = 8%. Year 2: 27 ÷ 540 = 0.05 = 5% (dividing by 500 again would give 5.4%, which is wrong).
6 A town’s population rose by 60% to 4000 people. What was the population before the rise?
Show worked solution
Old × 1.6 = 4000, so old = 4000 ÷ 1.6 = 2500. (Taking 60% off 4000 gives 1600 — the reverse trap.)
Level 3 · Challenge
7 A price changed from $350 to $420.1 The percentage increase is 20%.
2 A 20% decrease would take $420 back to $350.
3 $420 is 120% of $350.
Which statements are correct?
2 A 20% decrease would take $420 back to $350.
3 $420 is 120% of $350.
Which statements are correct?
Show worked solution
70 ÷ 350 = 0.2, a 20% increase (1 ✓). 420 × 0.8 = $336, not $350; the decrease needed is 70 ÷ 420, about 16.7% (2 ✗). 350 × 1.2 = 420 (3 ✓). 1 and 3.
8 A $640 jacket is reduced by 37.5%. Find the sale price, and the percentage increase that would take it back to $640.
Show worked solution
640 × 0.625 = $400. To get back: 240 ÷ 400 = 0.6 = 60% (not 37.5%, because the increase is measured from $400).
9 A club’s membership grew by 20% in its first year and by 12.5% in its second year, reaching 2700 members. How many members did it start with?
Show worked solution
2700 ÷ 1.125 = 2400, and 2400 ÷ 1.2 = 2000. Check: 2000 × 1.2 = 2400 and 2400 × 1.125 = 2700. (Taking 32.5% off 2700 gives 1822.5 — wrong twice over.)