Ratio in Daily Life
A ratio compares two quantities of the same kind. You use ratios every day without even realising it — when mixing lemonade (water to lemon juice), when reading a map (map distance to real distance), or when sharing sweets among friends.
In this topic, you will see how ratios appear in cooking, shopping, maps, sports, art, and everyday activities. Understanding ratios in daily life makes you better at problem-solving and decision-making.
Remember: a ratio compares two quantities and tells you "how many times" one quantity is of another.
What is Ratio in Daily Life?
Definition: A ratio is a way of comparing two quantities by division. It tells how much of one thing there is compared to another.
How to write a ratio:
- a to b is written as a : b or a/b.
- Both quantities must be in the same unit.
- A ratio has no unit — it is a pure number.
- Ratios should be in simplest form (divide both by their HCF).
Examples of ratios in daily life:
- Recipe: sugar to flour = 1 : 3
- Class: boys to girls = 15 : 20 = 3 : 4
- Map: 1 cm represents 5 km → scale 1 : 500,000
Types and Properties
1. Ratios in Cooking and Recipes
- Recipes give ingredients in ratios. Lemonade: water to lemon juice to sugar = 4 : 1 : 1.
- To scale a recipe, multiply all parts of the ratio by the same number.
2. Ratios in Maps and Models
- Map scale 1 : 50,000 means 1 cm on map = 50,000 cm (500 m) in reality.
- A model car at 1 : 20 scale means the model is 20 times smaller than the real car.
3. Ratios in Shopping
- Comparing prices: Rs. 80 for 2 kg vs Rs. 150 for 5 kg → which is cheaper per kg?
- Discounts: 30% off means you pay 70% → ratio of discount to price = 30 : 70 = 3 : 7.
4. Ratios in Sports
- Win-loss ratio: Won 8, Lost 2 → ratio 8 : 2 = 4 : 1.
- Batting average and run rates use ratios.
5. Ratios in Mixing
- Paint mixing: red to white = 1 : 4 gives light pink.
- Cement to sand = 1 : 3 for mortar.
Solved Examples
Example 1: Example 1: Mixing juice
Problem: To make orange juice, mix concentrate and water in the ratio 1 : 4. How much water for 3 cups of concentrate?
Solution:
- Ratio: 1 part concentrate : 4 parts water.
- For 3 cups concentrate: water = 3 × 4 = 12 cups.
Answer: 12 cups of water.
Example 2: Example 2: Recipe scaling
Problem: A cake recipe for 4 people needs 200 g flour and 100 g sugar. How much for 10 people?
Solution:
- Scale factor = 10/4 = 2.5.
- Flour = 200 × 2.5 = 500 g.
- Sugar = 100 × 2.5 = 250 g.
Answer: 500 g flour, 250 g sugar.
Example 3: Example 3: Map reading
Problem: On a map, 1 cm = 5 km. Two cities are 8 cm apart on the map. Find the real distance.
Solution:
- Real distance = 8 × 5 = 40 km.
Answer: 40 km.
Example 4: Example 4: Boys and girls
Problem: A class has 18 boys and 12 girls. Find the ratio of boys to girls in simplest form.
Solution:
- 18 : 12. HCF of 18 and 12 = 6.
- 18/6 : 12/6 = 3 : 2.
Answer: 3 : 2
Example 5: Example 5: Price comparison
Problem: Shop A: 3 kg apples for Rs. 240. Shop B: 5 kg apples for Rs. 350. Which is cheaper?
Solution:
- Shop A: Rs. 240/3 = Rs. 80 per kg.
- Shop B: Rs. 350/5 = Rs. 70 per kg.
Answer: Shop B is cheaper (Rs. 70/kg vs Rs. 80/kg).
Example 6: Example 6: Sports ratio
Problem: A team won 12 matches and lost 4. Find the win-to-loss ratio.
Solution:
- 12 : 4. HCF = 4.
- 12/4 : 4/4 = 3 : 1.
Answer: Win-to-loss ratio = 3 : 1.
Example 7: Example 7: Mixing paint
Problem: To get green paint, mix blue and yellow in ratio 2 : 3. If you need 10 litres total, how much of each?
Solution:
- Total parts = 2 + 3 = 5.
- Blue = (2/5) × 10 = 4 litres.
- Yellow = (3/5) × 10 = 6 litres.
Answer: 4 litres blue, 6 litres yellow.
Example 8: Example 8: Time ratio
Problem: Aisha studies 2 hours and plays 30 minutes daily. Find the ratio of study to play.
Solution:
- Convert to same unit: 2 hours = 120 minutes.
- 120 : 30 = 4 : 1.
Answer: 4 : 1
Example 9: Example 9: Model scale
Problem: A model building is 30 cm tall. The real building is 15 m tall. Find the scale.
Solution:
- Real height = 15 m = 1500 cm.
- Scale = 30 : 1500 = 1 : 50.
Answer: Scale = 1 : 50.
Example 10: Example 10: Sharing in ratio
Problem: Rs. 500 is shared between Ram and Shyam in ratio 3 : 2. How much does each get?
Solution:
- Total parts = 3 + 2 = 5.
- Ram = (3/5) × 500 = Rs. 300.
- Shyam = (2/5) × 500 = Rs. 200.
Answer: Ram = Rs. 300, Shyam = Rs. 200.
Real-World Applications
Cooking: Every recipe is based on ratios. The ratio of ingredients determines the taste and texture of food.
Maps and Navigation: Map scales are ratios that help convert map distances to real distances and vice versa.
Shopping: Comparing unit prices, calculating discounts, and figuring out the best deal all use ratios.
Art and Design: The golden ratio (approximately 1 : 1.618) is used in paintings, architecture, and design for visual appeal.
Science: Chemical formulas, speed calculations, and density all involve ratios of quantities.
Key Points to Remember
- A ratio compares two quantities of the same kind.
- Written as a : b. Both quantities must be in the same unit.
- A ratio has no unit — it is a pure comparison.
- Always simplify to the lowest terms using HCF.
- To share an amount in ratio a : b: each share = (part/total parts) × amount.
- Ratios appear in cooking, maps, shopping, sports, and mixing.
- Both parts of a ratio can be multiplied or divided by the same number without changing the ratio.
- Equivalent ratios: 1:2 = 2:4 = 3:6 = 5:10.
Practice Problems
- A recipe needs flour and sugar in ratio 5 : 2. If you use 250 g of flour, how much sugar?
- On a map, 2 cm = 100 km. How far apart are two cities that are 7 cm apart on the map?
- A class has 24 boys and 16 girls. Find the ratio of boys to total students.
- Mix red and blue paint 3 : 5 to get purple. How much of each for 16 litres?
- Share Rs. 1200 between A and B in ratio 5 : 7.
- A model train is 25 cm long. The real train is 25 m long. Find the scale.
- Ravi walks 4 km in 1 hour. Sita walks 3 km in 1 hour. Find the ratio of their speeds.
- Tea to milk ratio is 3 : 1. If you make 2 litres of tea, how much milk?
Frequently Asked Questions
Q1. What is a ratio?
A ratio compares two quantities by division. It tells how many times one quantity is of another. For example, 3 : 5 means for every 3 of the first, there are 5 of the second.
Q2. Why must both quantities be in the same unit?
Because ratio is a comparison. Comparing 2 km with 500 m directly does not make sense. Convert both to the same unit first: 2 km = 2000 m, then ratio = 2000 : 500 = 4 : 1.
Q3. Does order matter in a ratio?
Yes. The ratio of boys to girls (3:2) is different from the ratio of girls to boys (2:3). Always match the order to what the question asks.
Q4. How do I simplify a ratio?
Divide both parts by their HCF. For 18 : 12, HCF = 6, so 18/6 : 12/6 = 3 : 2.
Q5. What are equivalent ratios?
Ratios that represent the same comparison. 1:2, 2:4, 3:6, 5:10 are all equivalent — they all mean 'half'.
Q6. How do I share an amount in a given ratio?
Add the ratio parts to get total parts. Each person's share = (their ratio part / total parts) × amount. For Rs. 600 in 2:3: total = 5, first gets 2/5 × 600 = Rs. 240, second gets 3/5 × 600 = Rs. 360.
Q7. Can a ratio have more than two parts?
Yes. For example, the ratio of flour : sugar : butter = 3 : 2 : 1. This means for every 3 parts flour, use 2 parts sugar and 1 part butter.
Q8. Is ratio the same as fraction?
Related but not the same. The ratio 3:5 can be written as the fraction 3/5. But a ratio compares part to part, while a fraction usually compares part to whole.
