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By Ankit Gupta
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Updated on 11 Jun 2025, 18:16 IST
Chapter 9 of RD Sharma Class 7 Maths focuses on the important concepts of Ratio and Proportion, which are fundamental topics in mathematics. Understanding ratios and proportions helps students in comparing quantities and finding relationships between them. These concepts play a significant role in everyday life, as they are used to compare prices, quantities in recipes, and even in real-life situations like sharing things between friends.
In simple terms, a ratio is a way to compare two or more quantities. For example, if there are 2 apples and 3 oranges, we can say the ratio of apples to oranges is 2:3. This comparison helps in understanding how much one quantity is in relation to another.
A proportion, on the other hand, is an equation that shows two ratios are equal. For example, if the ratio of apples to oranges is 2:3, and the ratio of mangoes to bananas is also 2:3, we can say the ratios are in proportion. This concept helps in solving problems where we need to find an unknown quantity, making it an essential skill in mathematics.
In this chapter, students will learn how to solve problems related to both ratio and proportion, using methods that involve simple calculations and logical thinking. The chapter covers various topics, such as finding the value of an unknown quantity when given a proportion, simplifying ratios, and solving word problems based on real-life situations.
To make it easier for students to understand, RD Sharma provides step-by-step solutions to problems, helping them grasp the concepts better. These solutions are designed to explain each step clearly, ensuring that students can follow along and solve similar problems on their own. By the end of the chapter, students will have a strong understanding of how ratios and proportions work, allowing them to tackle related problems with confidence.
With the help of RD Sharma Solutions, students will not only understand the theory behind ratios and proportions but also develop problem-solving skills that will be useful in higher classes. The chapter is an important part of Class 7 Maths, laying the foundation for future topics that involve proportional reasoning.
RD Sharma Class 7 Chapter 9 PDF includes detailed solutions, examples, and extra questions to help you master real numbers and other topics. Click here to download the RD Sharma Class 7 Chapter 9 PDF.
In this chapter, students will learn about decimals and how to perform basic operations with them. The solutions provided here are detailed and easy to follow, helping students understand each concept thoroughly.
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Q1. If x: y = 3: 5, find the ratio 3x + 4y : 8x + 5y
Solution:
Given x: y = 3: 5
We can write this as:
x/y = 3/5
So, 5x = 3y, and x = 3y/5
Substitute x in 3x + 4y : 8x + 5y:
3x + 4y : 8x + 5y = 3(3y/5) + 4y : 8(3y/5) + 5y
= (9y + 20y)/5 : (24y + 25y)/5
= 29y/5 : 49y/5
= 29y : 49y
= 29 : 49
Q2. If x: y = 8: 9, find the ratio (7x - 4y) : 3x + 2y
Solution:
Given x: y = 8: 9
We can write this as:
x/y = 8/9
So, 9x = 8y, and x = 8y/9
Substitute x in (7x - 4y) : 3x + 2y:
(7x - 4y) : 3x + 2y = 7(8y/9) - 4y : 3(8y/9) + 2y
= (56y - 36y)/9 : 42y/9
= 20y/9 : 42y/9
= 20y : 42y
= 20 : 42
= 10 : 21
Q3. If two numbers are in the ratio 6: 13 and their L.C.M is 312, find the numbers
Solution:
Let the numbers be 6x and 13x
The LCM of 6x and 13x is 78x
So, 78x = 312, x = 4
The numbers are 6x = 6(4) = 24 and 13x = 13(4) = 52
Q4. Two numbers are in the ratio 3: 5. If 8 is added to each number, the ratio becomes 2: 3. Find the numbers
Solution:
Let the numbers be 3x and 5x
If 8 is added to each number, then the ratio becomes 2: 3:
(3x + 8) : (5x + 8) = 2 : 3
By solving, x = 8
The numbers are 3x = 3(8) = 24 and 5x = 5(8) = 40
Q5. What should be added to each term of the ratio 7: 13 so that the ratio becomes 2: 3?
Solution:
Let the number to be added be x
(7 + x) : (13 + x) = 2 : 3
By solving, x = 5
Q6. Three numbers are in the ratio 2: 3: 5 and the sum of these numbers is 800. Find the numbers
Solution:
The sum of the ratio terms = 2 + 3 + 5 = 10
The first number = (2/10) × 800 = 160
The second number = (3/10) × 800 = 240
The third number = (5/10) × 800 = 400
The three numbers are 160, 240, and 400
Q7. The ages of two persons are in the ratio 5: 7. Eighteen years ago their ages were in the ratio 8: 13. Find their present ages
Solution:
Let the present ages be 5x and 7x
18 years ago, their ages were in the ratio 8: 13:
(5x - 18) / (7x - 18) = 8 / 13
By solving, x = 10
The present ages are 5x = 5(10) = 50 years and 7x = 7(10) = 70 years
Q8. Two numbers are in the ratio 7: 11. If 7 is added to each of the numbers, the ratio becomes 2: 3. Find the numbers
Solution:
Let the numbers be 7x and 11x
If 7 is added to each number, then:
(7x + 7) / (11x + 7) = 2 / 3
By solving, x = 7
The numbers are 7x = 7(7) = 49 and 11x = 11(7) = 77
Q9. Two numbers are in the ratio 2: 7. If the sum of the numbers is 810, find the numbers
Solution:
Given the sum of the numbers = 810
The sum of the terms in the ratio = 2 + 7 = 9
The first number = (2/9) × 810 = 180
The second number = (7/9) × 810 = 630
Q10. Divide Rs 1350 between Ravish and Shikha in the ratio 2: 3
Solution:
The total amount is Rs 1350
Ravish's share = (2/5) × 1350 = Rs 540
Shikha's share = (3/5) × 1350 = Rs 810
Q11. Divide Rs 2000 among P, Q, and R in the ratio 2: 3: 5
Solution:
The total amount is Rs 2000
P’s share = (2/10) × 2000 = Rs 400
Q’s share = (3/10) × 2000 = Rs 600
R’s share = (5/10) × 2000 = Rs 1000
Q12. The boys and girls in a school are in the ratio 7: 4. If the total strength of the school is 550, find the number of boys and girls
Solution:
The total number of boys = (7/11) × 550 = 350
The total number of girls = (4/11) × 550 = 200
Q13. The ratio of monthly income to the savings of a family is 7: 2. If the savings are Rs. 500, find the income and expenditure
Solution:
The savings = 2x, so x = 250
Income = 7x = Rs 1750
Expenditure = Income – savings = Rs 1750 – Rs 500 = Rs 1250
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A ratio is a comparison of two quantities of the same kind by division. In Chapter 9, you learn how to express ratios between two or more numbers and solve problems related to them.
To solve ratio problems, first express the quantities in simplest form, then apply basic operations like addition, subtraction, multiplication, or division, depending on the problem. RD Sharma provides step-by-step solutions for better understanding.
A proportion is an equation that states that two ratios are equal. For example, if a/b = c/d, then a, b, c, and d are in proportion. This chapter helps you solve proportion problems through methods like cross-multiplication.
RD Sharma Solutions break down proportion problems into manageable steps, helping students understand how to set up equations and solve them efficiently using cross-multiplication or equivalent ratios.
Yes, RD Sharma Solutions for Class 7 Maths are designed in a way that students can understand the concepts and methods on their own. The explanations are simple and provide clear, step-by-step solutions to each problem.
Equivalent ratios are ratios that represent the same relationship. RD Sharma covers how to find equivalent ratios by multiplying or dividing both terms of a ratio by the same number.
Yes, the chapter includes several real-life applications such as sharing a quantity between people in a specific ratio or scaling recipes for different numbers of servings. RD Sharma helps relate these concepts to practical situations.
Practice by solving the exercises in RD Sharma, starting with simpler problems and gradually moving to more complex ones. The solutions guide you through each step, ensuring that you grasp the concepts thoroughly.