Ratio Word Problems
Ratios are used in everyday life — sharing sweets among friends, mixing ingredients in a recipe, or scaling up a drawing. When these situations are described in words, they become ratio word problems.
To solve ratio word problems, you need to understand what is being compared and then use the ratio to find the answer.
In Class 6, you will learn the main types of ratio word problems and the steps to solve them.
What is Ratio Word Problems - Grade 6 Maths (Ratio and Proportion)?
Main types of ratio word problems:
- Type 1: Dividing a quantity in a given ratio. Example: Divide 40 sweets between two friends in the ratio 3:5.
- Type 2: Finding one quantity when the ratio and the other quantity are known. Example: Boys to girls ratio is 2:3 and there are 12 boys. How many girls?
- Type 3: Finding the total from the ratio. Example: Ratio of red to blue marbles is 4:7. There are 28 blue marbles. Find total marbles.
Ratio Word Problems Formula
Steps to divide a quantity in a given ratio a:b:
- Find the total parts = a + b.
- Find the value of one part = Total quantity ÷ total parts.
- First share = a × one part.
- Second share = b × one part.
First share = (a / (a+b)) × Total
Second share = (b / (a+b)) × Total
Steps when one part of the ratio is known:
- If a:b and the value of 'a' is given, find the multiplier = given value ÷ a.
- Value of b = b × multiplier.
- Total = (a + b) × multiplier.
Types and Properties
Common ratio word problem situations:
- Sharing money: Two or more people share an amount in a ratio.
- Mixing: Two ingredients are mixed in a ratio (e.g., juice and water).
- Counting: Boys and girls in a class, or different coloured objects in a collection.
- Scaling: Increasing or decreasing a recipe while keeping the ratio the same.
Solved Examples
Example 1: Dividing in a Ratio
Problem: Divide Rs 200 between Anu and Riya in the ratio 3:2.
Solution:
- Total parts = 3 + 2 = 5
- One part = 200 ÷ 5 = Rs 40
- Anu's share = 3 × 40 = Rs 120
- Riya's share = 2 × 40 = Rs 80
Answer: Anu gets Rs 120 and Riya gets Rs 80.
Example 2: Finding the Other Quantity
Problem: The ratio of boys to girls in a class is 3:4. There are 15 boys. How many girls are there?
Solution:
- Boys part = 3, Girls part = 4.
- Multiplier = 15 ÷ 3 = 5
- Number of girls = 4 × 5 = 20
Answer: There are 20 girls.
Example 3: Finding Total from Ratio
Problem: Red and blue marbles are in the ratio 2:5. There are 35 blue marbles. Find the total number of marbles.
Solution:
- Blue part = 5, so multiplier = 35 ÷ 5 = 7.
- Red marbles = 2 × 7 = 14
- Total = 14 + 35 = 49
Answer: Total marbles = 49.
Example 4: Mixing Problem
Problem: A juice drink is made by mixing juice and water in the ratio 1:3. If 2 litres of juice is used, how much water is needed?
Solution:
- Juice : Water = 1:3
- Multiplier = 2 ÷ 1 = 2
- Water = 3 × 2 = 6 litres
Answer: 6 litres of water is needed.
Example 5: Three-Way Division
Problem: Divide 60 chocolates among three children in the ratio 2:3:5.
Solution:
- Total parts = 2 + 3 + 5 = 10
- One part = 60 ÷ 10 = 6
- First child = 2 × 6 = 12
- Second child = 3 × 6 = 18
- Third child = 5 × 6 = 30
Answer: 12, 18, and 30 chocolates.
Example 6: Income and Savings
Problem: Ravi's income and savings are in the ratio 5:1. If his income is Rs 25,000, find his savings.
Solution:
- Income part = 5, Savings part = 1
- Multiplier = 25,000 ÷ 5 = 5,000
- Savings = 1 × 5,000 = Rs 5,000
Answer: Savings = Rs 5,000.
Example 7: Finding the Ratio
Problem: There are 18 apples and 12 oranges. Find the ratio of apples to oranges in simplest form.
Solution:
Ratio = 18:12. HCF = 6.
18 ÷ 6 : 12 ÷ 6 = 3:2
Example 8: Scaling a Recipe
Problem: A recipe for 4 people uses 200 g flour and 100 g sugar (ratio 2:1). How much flour and sugar for 10 people?
Solution:
Scale factor = 10 ÷ 4 = 2.5
- Flour = 200 × 2.5 = 500 g
- Sugar = 100 × 2.5 = 250 g
The ratio is still 2:1 (500:250 = 2:1).
Answer: 500 g flour and 250 g sugar.
Real-World Applications
Where ratio word problems appear:
- Sharing: Dividing pocket money, inheritance, or profits.
- Cooking: Scaling recipes up or down.
- Business: Dividing profit between partners.
- Science: Mixing chemicals in a given ratio.
- Maps: Converting map distances to real distances using scale ratios.
Key Points to Remember
- To divide in a ratio a:b: total parts = a + b, one part = total ÷ (a+b).
- When one part of the ratio is known, find the multiplier first.
- Check your answer: the shares must add up to the total.
- Ratios can have three or more parts (a:b:c). The method is the same.
- Always simplify the ratio in your final answer unless told otherwise.
- The order of the ratio matters — 3:5 is not the same as 5:3.
Practice Problems
- Divide Rs 350 between two friends in the ratio 4:3.
- The ratio of cats to dogs in a shelter is 5:3. There are 20 cats. How many dogs?
- Divide 72 books among three shelves in the ratio 1:2:3.
- Juice and water are mixed in the ratio 2:5. If there are 500 ml of water, how much juice was used?
- A class has boys and girls in the ratio 7:5. There are 60 students in total. How many boys and girls?
- Two numbers are in the ratio 3:8. Their sum is 55. Find both numbers.
Frequently Asked Questions
Q1. How do I divide a number in a given ratio?
Add the parts of the ratio to get total parts. Divide the number by total parts to get one part. Multiply each ratio number by one part to get the shares.
Q2. What is a multiplier in ratio problems?
The multiplier is the number you multiply each ratio part by to get the actual values. If the ratio is 2:3 and the first quantity is 10, the multiplier is 10 ÷ 2 = 5.
Q3. How do I check my answer?
Add all the shares together. The total should equal the original quantity. Also check that the shares are in the correct ratio.
Q4. Can I divide in a ratio of three or more parts?
Yes. For ratio a:b:c, total parts = a + b + c. One part = total ÷ (a+b+c). Then multiply each part number by the value of one part.
Q5. What if the ratio has decimals?
First simplify the ratio to whole numbers by multiplying both parts by 10 or 100. Then solve as usual.
Q6. What if I need to find the total from a ratio?
If you know one part of the ratio and its actual value, find the multiplier. Then total = (sum of all ratio parts) × multiplier.
