Question: In 2018 a car cost $\usd{}45\,000$; in 2025 the same car costs $\usd{}85\,000$. (a) Find the percentage increase, to 1 d.p. (b) The dealer then cuts the 2025 price by $5\%$ — find the new price.

Step 1. (a) Percentage change always divides by the original value:

Step 2.

Step 3. (b) A $5\%$ cut leaves $95\%$:

Step 4. Note the asymmetry: the cut is $5\%$ of the 2025 price ($\usd{}4\,250$), which is much more than $5\%$ of the 2018 price — every percentage lives on its own base.

The identical arithmetic runs profit and loss: profit% $= \dfrac{\text{selling} - \text{cost}}{\text{cost}} \times 100\%$ — cost price on the bottom.

⚠ Watch out: Dividing by the new value ($\frac{40000}{85000} = 47.1\%$) is the standard error — the original is always the base. And a $88.9\%$ rise followed by a $5\%$ cut is not an $83.9\%$ net rise; multipliers ($\times 1.889 \times 0.95$), not additions.

Question: (a) The rate is S$1.2470 = US\usd{}1. How many US dollars for S\usd{}1000? (b) The rate is HK\usd{}100 = S\usd{}21.10. How many Singapore dollars for HK\usd{}10 000?

Step 1. (a) The rate says every US dollar costs S\usd{}1.2470. Converting S\usd{} into US\usd{} therefore divides:

Step 2. Sense-check: the US dollar is the stronger unit here, so the number should shrink — $801.92 < 1000$. ✓

Step 3. (b) Scale the given rate up to the amount held. From HK\usd{}100 to HK\usd{}10 000 is $\times 100$:

Step 4. Exchange rates are ratios — either scale the rate (Step 3) or form the unit rate first (S\usd{}0.2110 per HK\usd{}1) and multiply. Both give S\usd{}2110.

⚠ Watch out: Multiply-or-divide is where exchange questions die. Anchor on the rate's meaning: S\usd{}1.2470 per US\usd{}1 means S\usd{} → US\usd{} divides, US\usd{} → S\usd{} multiplies. When in doubt, sanity-check the size of the answer against which currency is stronger.