RD Sharma Solutions for Class 6 Maths Chapter 9 Ratio, Proportion and Unitary Method

RD Sharma Solutions for Class 6 Maths Chapter 9: Understanding ratio, proportion, and unitary method is crucial for building strong mathematical skills in Class 6. Chapter 9 of RD Sharma Solutions for Class 6 covers these concepts in depth, providing a clear and easy approach to learning. A ratio explains how many times one quantity includes another, while a proportion shows that two ratios are equal. The unitary method helps solve problems by finding the value of a single unit first, then scaling it up. 

Students following the CBSE syllabus will find this chapter particularly important as it is a key part of their curriculum. The RD Sharma Solutions offer detailed explanations, plenty of practice exercises, and guidance to help students score better. Free downloadable PDFs are also available on platforms like Infinity Learn. 

For extra practice, resources such as the ratio, proportion and unitary method worksheet Class 6 with answers and Ratio and Proportion Class 6 Extra Questions with answers make it easier for students to master these topics confidently. Using these tools along with NCERT solutions ensures a strong foundation in mathematics, making exam preparation smooth and effective.

RD Sharma Solutions for Class 6 Maths Chapter 9 Overview

Download RD Sharma Solutions for Chapter 9 Ratio, Proportion and Unitary Method PDF Here

The RD Sharma Class 6 Mathematics Chapter 9 PDF is now available for download, offering comprehensive solutions to help students build a strong foundation in these essential mathematical concepts. This downloadable resource provides step-by-step solutions to all exercise problems, making it easier to understand complex ratio calculations and proportional relationships. 

Regular practice with these solved examples can significantly improve your problem-solving abilities and boost your confidence for upcoming assessments.
The Chapter 9 PDF includes detailed explanations for each concept, practice worksheets, and additional questions that align perfectly with your school curriculum. Students struggling with mathematics can benefit from the clear, concise approach that breaks down difficult concepts into manageable parts.

Topics Covered in Class 6 Maths Chapter 9 Ratio, Proportion and Unitary Method 

This chapter covers three fundamental mathematical concepts:

1. Ratios
   • Definition: The comparison of two quantities of the same type by dividing one by the other is known as a ratio.
   • Key aspects: Simplest form, real-life applications, inverse ratios, equivalent ratios
   • Skills taught: Simplification, comparison, and ordering of ratios
2. Proportion
   • Definition: Equality between two ratios
   • Key properties: Means and extremes, continued proportion
   • Problem-solving technique: Cross-multiplication
3. Unitary Method
   • Two-step approach: Find value of one unit, then multiply for required units
   • Applications: Cost, time, distance, and quantity calculations

The chapter includes practical applications in daily life (shopping, cooking, budgeting) and provides comprehensive practice through solved examples, extra questions, and worksheets to reinforce learning and exam preparation.

RD Sharma Textbook Solutions for Class 6 Maths Chapter 9

Exercise 9.1 page: 9.5

1. Express the following situations using ratios:

(i) In a certain class, the count of girls listed in the board exam merit list is twice the count of boys.

(ii) The number of students who passed the mathematics test is two-thirds of the total number of students who appeared for the test.

Solutions:

(i) The ratio of the number of girls to the number of boys on the merit list is 2 : 1.

(ii) The ratio of students passing the mathematics test to those who appeared is 2 : 3.

2. Express the following ratios in the language of everyday life:

(i) In a factory, the proportion of defective pencils to perfect pencils is 1 : 9.

(ii) In India, the proportion between the number of villages and the number of cities is approximately 2000 : 1.

Solutions:

(i) The number of faulty pencils produced in the factory is one-ninth of the number of good pencils manufactured.

(ii) The number of villages in India is around 2000 times greater than the number of cities.

3. Express the following ratios in their lowest (simplest) form:

(i) 60: 72

(ii) 324: 144

(iii) 85: 391

(iv) 186: 403

Solution:

(i) 60: 72

It can be written as 60/72

As we are aware that HCF of 60 and 72 is 12

By dividing the term by 12 we get

(60/72) × (12/12) = 5/6

So we get 60: 72 = 5: 6

(ii) 324: 144

It can be written as 324/144

As we are aware that the HCF of 324 and 144 is 36

By dividing the term by 36 we get

(324/144) × (36/36) = 9/4

So we get 324: 144 = 9: 4

(iii) 85: 391

It can be written as 85/391

As we are aware that the HCF of 85 and 391 is 17

By dividing the term by 17 we get

(85/391) × (17/17) = 5/23

So we get 85: 391 = 5: 23

(iv) 186: 403

It can be written as 186/403

As we are aware that the HCF of 186 and 403 is 31

By dividing the term by 31 we get

(186/403) × (31/31) = 6/13

So we get 186: 403 = 6: 13

4. Simplify the following ratios:

(i) 75 paise : ₹3
Convert both values to the same unit. Since ₹1 = 100 paise, ₹3 = 300 paise.
So, the ratio becomes 75 : 300
Dividing both by 75 → 1 : 4

(ii) 35 minutes : 45 minutes
Both are in the same unit already.
Divide by 5 → 7 : 9

(iii) 8 kilograms : 400 grams
Convert kilograms to grams: 8 kg = 8000 grams
So, the ratio is 8000 : 400
Divide by 400 → 20 : 1

(iv) 48 minutes : 1 hour
1 hour = 60 minutes
Ratio becomes 48 : 60
Divide by 12 → 4 : 5

(v) 2 metres : 35 cm
Convert metres to centimetres: 2 m = 200 cm
Now, ratio is 200 : 35
Divide by 5 → 40 : 7

(vi) 35 minutes : 45 seconds
Convert minutes to seconds: 35 × 60 = 2100 seconds
Ratio becomes 2100 : 45
Divide by 15 → 140 : 3

(vii) 2 dozen : 3 scores
1 dozen = 12, 1 score = 20
So, 2 dozen = 24, 3 scores = 60
Ratio is 24 : 60
Divide by 12 → 2 : 5

(viii) 3 weeks : 3 days
Convert weeks to days: 3 × 7 = 21 days
Ratio becomes 21 : 3
Divide by 3 → 7 : 1

(ix) 48 minutes : 2 hours 40 minutes
2 hours = 120 minutes, total = 160 minutes
Ratio becomes 48 : 160
Divide by 16 → 3 : 10

(x) 3 m 5 cm : 35 cm
Convert 3 m 5 cm = 305 cm
Ratio becomes 305 : 35
Divide by 5 → 61 : 7

5. Find the Ratio in Simplest Form
(i) 3.2 m : 56 m
Convert to same unit and divide directly:
3.2 : 56 → Divide both by 1.6 → 2 : 35

(ii) 10 m : 25 cm
Convert 10 m to cm = 1000 cm
So, ratio becomes 1000 : 25
Divide by 25 → 40 : 1

(iii) 25 paise : ₹60
Convert ₹60 to paise = 6000
Ratio is 25 : 6000
Divide by 25 → 1 : 240

(iv) 10 litres : 0.25 litre
Divide both by 0.25 → 40 : 1

6. Real-Life Ratio Problems

1. School Strength – Boys vs Girls
   Total boys = 1168, girls = 1095
   Ratio of boys to girls = 1168 : 1095
   HCF = 73 → Simplified ratio = 16 : 15
2. Monthly Incomes
   Avinash earns ₹12,000/month; his wife earns ₹15,000/month

(i) Ratio of Avinash’s income to wife’s = 12000 : 15000 → 4 : 5
(ii) Total income = ₹27,000 → Ratio of Avinash to total = 12000 : 27000 → 4 : 9

3. Office Staff Ratio
   Total employees = 72, Men = 28, Women = 72 - 28 = 44

(i) Men : Women = 28 : 44 → 7 : 11
(ii) Men : Total = 28 : 72 → 7 : 18
(iii) Total : Women = 72 : 44 → 18 : 11

4. Measuring Tape Dimensions
   Length = 10 m = 1000 cm, Width = 2.4 cm
   Ratio = 1000 : 2.4 → Divide both by 0.8 → 1250 : 3
5. Office Timing & Break
   Working hours = 9 AM to 5 PM = 8 hours = 480 minutes
   Lunch = 30 minutes
   Ratio = 30 : 480 → 1 : 16
6. Comparing Travel Speeds
   Bullock-cart: 24 km in 3 hours = 8 km/h
   Train: 120 km in 2 hours = 60 km/h
   Ratio = 8 : 60 → 2 : 15
7. Monthly Savings
   Income = ₹955, Savings = ₹185 → Expenditure = ₹770

(i) Savings : Income = 185 : 955 → 37 : 191
(ii) Income : Expenditure = 955 : 770 → 191 : 154
(iii) Savings : Expenditure = 185 : 770 → 37 : 154

Tips to Prepare for RD Sharma Solutions for Class 6 Maths Chapter 9

1. Master the Fundamentals First
Understanding the core concepts of ratio, proportion, and unitary method forms the foundation for solving all problems in this chapter. Take time to grasp these basics thoroughly before attempting complex problems.

2. Practice Systematic Problem-Solving
When working with ratio and proportion problems, follow a step-by-step approach:

• Identify what the question is asking for
• Extract all relevant data carefully
• Set up your ratios or proportions clearly
• Cross-multiply accurately to find the unknown value

3. Watch Out for Common Mistakes
Students often confuse ratio with fraction or make errors when inverting ratios. Remember that a ratio of 2:3 is different from 3:2, and ratio comparisons must always be made in the same units.

4. Use Cross-Multiplication Effectively
The cross-multiplication technique is essential for solving proportion problems. Practice this method extensively and double-check your calculations to avoid arithmetic errors.

5. Practice All Exercise Types
Chapter 9 offers diverse problem sets across its exercises:

• Exercise 9.1 (12 questions) covers fundamental ratio concepts
• Exercise 9.2 (3 questions) covers proportion basics
• Exercise 9.3 (12 questions) addresses proportion applications
• Exercise 9.4 (15 questions) deals with unitary method problems

6. Create Visual Representations
For complex ratio problems, try creating diagrams or tables to organize information. Visual aids can help clarify relationships between quantities and prevent mistakes in calculations.

7. Apply Real-World Connections
Relate ratio and proportion concepts to everyday situations like recipe adjustments, scale models, or shopping discounts. This practical understanding will strengthen your problem-solving abilities.