Percentage

Percentage increase/decrease, finding the whole given a part and the percentage, discount, GST, and annual interest.

% increase/decreasefind the wholediscount & GST P2 · calc
% of amount = % ÷ 100 × whole % increase = (increase ÷ original) × 100% % decrease = (decrease ÷ original) × 100% Find whole = part ÷ % × 100
Question 1 — Percentage of a whole & discount
Short answer (2 marks) Paper 2 · calculator Discount & GST

A jacket costs $85 before discount. A shop offers a 20% discount, followed by a 9% GST on the discounted price. How much does James pay for the jacket?

$85 × 80% = $68 (after discount) $68 × 109% = $74.12 (final price) 20% off +9% GST
Discounted= $85 × (1 − 20%) = $85 × 0.80 = $68.00
After GST= $68 × (1 + 9%) = $68 × 1.09 = $74.12
James pays $74.12

Apply operations in sequence — discount first, then GST on the new price. Do NOT apply GST to the original $85. Multiplying by 1.09 is faster than finding 9% and adding it separately.

Question 2 — Percentage increase & decrease
Structured answer (3–4 marks) Paper 2 · calculator % increase / decrease

In January, a bookshop sold 450 books. In February, the number of books sold increased by 20%. In March, the number of books sold decreased by 25% compared to February.

(a) How many books were sold in March?
(b) What was the percentage change in books sold from January to March?

Jan 450 +20% Feb 540 −25% Mar ?
Feb sales= 450 × 1.20 = 540 books
(a) Mar= 540 × 0.75 = 405 books
(b) Change= 405 − 450 = −45 books (a decrease)
% change= 45 ÷ 450 × 100% = 10% decrease
(a) 405 books  |  (b) 10% decrease from January

The trap in part (b): +20% then −25% does NOT cancel out to −5%. Always compute the actual values first, then find % change against the original January figure.

Question 3 — Find the original (whole) given the part
Long answer (4–5 marks) Paper 2 · calculator Find the whole · reverse %

Mrs Lee spent 35% of her monthly salary on rent and 40% of the remainder on food. She saved the rest. If she saved $1170, how much is her monthly salary?

Monthly salary (100%) Rent (35%) Remainder (65%) Food (26%) Saved $1170 (39%)
RemainderAfter rent: 100% − 35% = 65% of salary
Food= 40% of remainder = 40% × 65% = 26% of salary
Saved= 65% − 26% = 39% of salary
39% = $1170→ 1% = $1170 ÷ 39 = $30
Salary= $30 × 100 = $3000
Monthly salary = $3000

Convert everything to a percentage of the original salary before working backwards. "40% of the remainder" means 40% of 65%, NOT 40% of the salary — compute it as a product first.