IGCSE · Practice questions · Percentages: change, reverse percentages

Multiply by the multiplier.

Six original Cambridge-style questions on percentages: amounts, changes, profit and loss, reverse percentages and deposits.

Original questions All questions on this page are original work, written in the Cambridge IGCSE style. They are not from past papers. They test the same concepts and skills the syllabus rewards.

The method

Turn the percentage into a multiplier.

Percentage of: multiply by the decimal: 18% $\to 0.18$.
As a percentage: $\dfrac{\text{part}}{\text{whole}} \times 100$, same units.
Increase/decrease: multiply by $1 \pm \dfrac{r}{100}$.
Percentage change: change ÷ ORIGINAL $\times 100$.
Reverse (Extended): divide the new amount by the multiplier.

Recall

[2 marks]

Work out (a) 18% of 350 (b) 135% of 80.

(a) $0.18 \times 350 = 63$ ✓
(b) $1.35 \times 80 = 108$ ✓

Recall

[2 marks]

Express 42 seconds as a percentage of 2 minutes.

2 minutes $= 120$ seconds. ✓
$\dfrac{42}{120} \times 100 = 35\%$ ✓

Calculation

[2 marks]

A bus fare of $\$85$ increases by 12%. Calculate the new fare.

Multiplier 1.12. ✓
$85 \times 1.12 = \$95.20$ ✓

Calculation

[2 marks]

Ella bought a car for $\$12\,500$ and sold it for $\$9800$. Calculate her percentage loss.

Loss $= 12\,500 - 9800 = \$2700$. ✓
$\dfrac{2700}{12\,500} \times 100 = 21.6\%$ ✓

Analysis

[2 marks]

(Extended) In a sale all prices are reduced by 30%. A jacket costs $\$63$ in the sale. Calculate its price before the sale.

The sale price is 70% of the original: multiplier 0.7. ✓
$63 \div 0.7 = \$90$ ✓

Analysis

[4 marks]

A laptop is priced at $\$750$.

Option A: pay cash and receive an 8% discount.
Option B: pay a 15% deposit, then 10 monthly payments of $\$66$.

(a) How much more does Option B cost than Option A?
(b) Write the total cost of Option B as a percentage of $\$750$.

Option A: $750 \times 0.92 = \$690$. ✓
Option B: deposit $0.15 \times 750 = \$112.50$; payments $10 \times 66 = \$660$; total $\$772.50$. ✓
(a) $772.50 - 690 = \$82.50$ ✓
(b) $\dfrac{772.50}{750} \times 100 = 103\%$ ✓

Mark this once you have attempted all six and checked your working. It records a Practiced badge on the topic and adds a one-time bonus. Revealing the solutions alone does not count.