Numerical aptitude · Ratios and averages
Ratio and proportion, made easy
💡 The idea
A ratio like 2 : 3 means “for every 2 of one, there are 3 of the other”. Think of it as parts.
🧭 The method: 3 steps
- Add the parts to get the total parts.
- Find one part: total amount ÷ total parts.
- Multiply one part by what each person gets.
🎬 Every kind of question, in pictures
Pick a kind. Guess the answer first, then watch the picture work it out. Tap any step to see it in the picture.
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✏️ Worked examples
Example 1. Share $100 in the ratio 2 : 3.
- Total parts = 2 + 3 = 5
- One part = 100 ÷ 5 = 20
- Shares: 2 × 20 = $40 and 3 × 20 = $60
Example 2. A:B = 2:3 and B:C = 4:5. Find A:B:C.
- B is 3 in one and 4 in the other. Make both 12.
- A:B = 2:3 → × 4 → 8:12
- B:C = 4:5 → × 3 → 12:15
- A:B:C = 8 : 12 : 15
Example 3. 3 pens cost $6. How much do 12 pens cost?
- 12 pens is 12 ÷ 3 = 4 times as many
- Cost = 6 × 4 = $24
⚠️ Where people go wrong
- Divide by the total parts, not one side of the ratio.
- When combining ratios, make the shared letter the same number first.
📌 Remember
- One part = total ÷ (sum of ratio numbers)