Solutions — Percentages and Applications

← Back to Questions

1. Q1 — Converting to percentages

   (a) 3/5 = 0.6 = 60%   (b) 7/8 = 0.875 = 87.5%   (c) 0.46 = 46%   (d) 1.025 = 102.5%   (e) 11/4 = 2.75 = 275%

2. Q2 — Percentage of a quantity

   (a) 0.20 × $350 = $70   (b) 0.08 × $1 200 = $96   (c) 0.125 × $640 = $80   (d) 0.025 × $8 400 = $210

3. Q3 — Multiplier method

   (a) $240 × 1.15 = $276   (b) $580 × 0.75 = $435   (c) $95 × 1.10 = $104.50   (d) $1 600 × 0.925 = $1 480

4. Q4 — Percentage change

   (a) (15 ÷ 50) × 100 = 30% increase   (b) (120 ÷ 800) × 100 = 15% decrease   (c) (1 500 ÷ 12 000) × 100 = 12.5% increase   (d) (18 ÷ 90) × 100 = 20% decrease

5. Q5 — GST calculations

   (a) $120 × 1.1 = $132   (b) Pre-GST = $231 ÷ 1.1 = $210. GST = $231 − $210 = $21.   (c) Pre-GST = $1 298 ÷ 1.1 = $1 180. The business pays $1 180.

6. Q6 — Discounts and markups

   (a) $340 × 1.40 = $476   (b) $890 × 0.82 = $729.80   (c) Sale price = 70% of original. Original = $84 ÷ 0.70 = $120

7. Q7 — Profit and loss

   (a) Profit = $15 000 − $12 500 = $2 500. Profit % = (2 500 ÷ 12 500) × 100 = 20%.   (b) Loss = $2.40 − $1.80 = $0.60/kg. Loss % = (0.60 ÷ 2.40) × 100 = 25%.   (c) Loss = $420 000 − $378 000 = $42 000. Loss % = (42 000 ÷ 420 000) × 100 = 10%.

8. Q8 — Successive percentage changes

   (a) $56 000 × 1.03 × 1.02 = $56 000 × 1.0506 = $58 833.60.   (b) Multiplier = 0.80 × 0.85 = 0.68. Equivalent single discount = 1 − 0.68 = 32%.   (c) Multiplier = 1.25 × 0.80 = 1.00. Overall change = 0% (back to original).

9. Q9 — Back-calculating original price

   (a) Original × 1.35 = $675 → Original = $675 ÷ 1.35 = $500.   (b) Original × 1.10 = $484 → Original = $484 ÷ 1.10 = $440.   (c) Final price = cost × 1.20 × 1.10 = cost × 1.32 = $158.40. Cost = $158.40 ÷ 1.32 = $120.

10. Q10 — Real-world percentage problem

    (a) Sale price = x × 1.60 × 0.75 = 1.20x = $108.   (b) x = $108 ÷ 1.20 = $90 (cost price).   (c) Price with GST = $108 × 1.10 = $118.80.   (d) Sale price (pre-GST) = $108. Cost = $90. Profit = $18. Profit % = (18 ÷ 90) × 100 = 20% profit on cost.