Class 7 Maths Chapter 7 Questions and Answers - Free PDF Download
In NCERT Solution for Class 7th Exercise 7.1, Students will learn how to calculate and interpret ratios, convert them into percentages, and understand their practical applications. The problems in Exercise 7.1 are designed to build a strong foundation in comparing quantities, which is essential for solving more complex problems in later exercises and real-life scenarios. students will develop a solid understanding of calculating probabilities in complex situations, which is vital for their academic and competitive exam preparations. Students can access the revised Class 7 Maths NCERT Solutions from our page which is prepared so that you can understand it easily.
Table of Content
Specially Class 7 Maths Chapter 7 Exercise 7.1 Question is important for students to understand it well. Students will learn how to calculate percentages, determine profit or loss in various transactions, and compute simple interest over different periods. Access Class 7 Maths Syllabus here.
Glance on NCERT Solutions Maths Chapter 7 Exercise 7.1 Class 7 | Vedantu
NCERT Solution for class 7th maths chapter 7 exercise 7.1 contains topics like the Meaning of Percentages, Converting Fractional Numbers to Percentages, Converting Decimals to Percentages, Converting Percentages to Fractions or Decimals, Fun with Estimation, and Use Of Percentages.
Meaning of Percentages: This section explains what percentages are and how they represent a part out of a whole (usually out of 100). Students will learn how the percentage symbol (%) is used.
Converting Fractional Numbers to Percentages: Here, Students will discover methods to convert fractions into percentages This might involve multiplying by 100 and adding a percent sign.
Converting Decimals to Percentages: Similar to fractions, this section teaches you how to convert decimal numbers into percentages. This might involve multiplying by 100 (or moving the decimal two places to the right) and adding a percent sign.
Converting Percentages to Fractions or Decimals: This section covers the reverse process - converting percentages back into fractions or decimals. You might learn to divide by 100 (or move the decimal two places to the left) and remove the percent sign.
Fun with Estimation: This section might introduce you to using percentages for estimation purposes. Students will learn to approximate values based on percentages.
Use of Percentages: This section explores real-life applications of percentages. You might see examples of how percentages are used in discounts, sales tax calculations, and other practical scenarios.
There are 10 questions in Exercise 7.1 Maths Class 7 Chapter 7 which experts at Vedantu fully solve.
Exercise 7.1
1. Convert the given fractional numbers to percent:
(a) $\frac{\text{1}}{\text{8}}$
Ans: A fractional number is given, $\frac{1}{8}$
$\frac{1}{8} =\frac{1}{8} \times 100 \%$
$=\frac{25}{2} \%=12.5 \%$
$\Rightarrow \frac{1}{8}=12.5 \%$
(b) $\frac{\text{5}}{\text{4}}$
Ans: A fractional number is given, $\frac{\text{5}}{\text{4}}$
$\frac{5}{4}=\frac{5}{4} \times 100 \%$
$=5 \times 25 \%$
$=125 \%$
$\Rightarrow \frac{5}{4}=125 \%$
(c) $\frac{\text{3}}{\text{40}}$
Ans: A fractional number is given, $\frac{\text{3}}{\text{40}}$
$\frac{3}{40}=\frac{3}{40} \times 100 \%$
$\quad=\frac{15}{2} \%$
$=7.5 \%$
$\Rightarrow \frac{3}{40}=7.5 \%$
(d) $\frac{\text{2}}{\text{7}}$
Ans: A fractional number is given, $\frac{\text{2}}{\text{7}}$
$\frac{2}{7}=\frac{2}{7} \times 100 \% $
$=\frac{200}{7} \%$
$=28 \frac{4}{7} \%$
$\Rightarrow \frac{2}{7}=28 \frac{4}{7} \%$
2. Convert the given decimal fractions to percents:
(a) $\text{0}\text{.65}$
Ans: A decimal fraction is given, needed to convert it into percentage from
$\Rightarrow 0.65=\frac{65}{100}$
$\Rightarrow 0.65=65 \%$
(b) $\text{2}\text{.1}$
Ans: A decimal fraction is given, needed to convert it into percentage from
$\Rightarrow 2.1=\frac{21}{10} \times 100 \%$
$\Rightarrow 2.1=210 \%$
(c) $\text{0}\text{.02}$
Ans: A decimal fraction is given, needed to convert it into percentage from
$\Rightarrow 0.02=\frac{2}{100}$
$\Rightarrow 0.02=2 \%$
(d) $\text{12}\text{.35}$
Ans: A decimal fraction is given, needed to convert it into percentage from
$\Rightarrow 12.35=\frac{1235}{100} \times 100 \%$
$\Rightarrow 12.35=1235 \%$
3. Estimate what part of the figure is coloured and hence find the percent which is coloured:
(i)
Ans: It is clear from the figure that the coloured part is $\text{= }\frac{\text{1}}{\text{4}}$
Therefore, the required percentage of coloured parts,
is $=\frac{1}{4} \times \frac{25}{25} $
$=\frac{25}{100} $
$=25 \%$
(ii)
Ans: It is clear from the figure that the coloured part is $\text{= }\frac{\text{3}}{\text{5}}$
Therefore, the required percentage of coloured parts,
is $\text{= }\frac{\text{3}}{\text{5}}\text{ }\!\!\times\!\!\text{ }\frac{\text{20}}{\text{20}}$
$\text{= }\frac{\text{60}}{\text{100}}$
$\text{= 60 }\%$
(iii)
Ans: It is clear from the figure that the coloured part is $\text{= }\frac{\text{3}}{\text{8}}$
Therefore, the required percentage of coloured parts,
is $\text{= }\frac{\text{3}}{\text{8}}\text{ }\!\!\times\!\!\text{ }\frac{\text{100}}{\text{100}}$
$\text{= }\frac{\text{300}}{\text{8}}\text{ }\%$
$\text{= 37}\text{.5 }\%$
4. Find:
(a) $\text{15 }\%$ of $\text{250}$
Ans: Needed to find the required percentage of the given number $\text{250}$ i.e.,
$\text{15 }\%\text{ }$ of $\text{250}$ $\text{= }\frac{\text{15}}{\text{100}}\text{ }\!\!\times\!\!\text{ 250}$
$\text{= 15 }\!\!\times\!\!\text{ 2}\text{.5}$
$\text{= 37}\text{.5}$
$\Rightarrow \text{ 15 }\%\text{ }$ of $\text{250}$$\text{= 37}\text{.5}$
(b). $\text{1 }\%$ of $\text{1}$ hour
Ans: Needed to find the required percentage i.e.,
$\text{1 }\%$ of $\text{1}$ hour $\text{= 1 }\%$ of $\text{60}$ minutes
$\text{= 1 }\%$ of $\text{60 }\!\!\times\!\!\text{ 60}$ seconds
$\text{= }\frac{\text{1}}{\text{100}}\text{ }\!\!\times\!\!\text{ 60 }\!\!\times\!\!\text{ 60}$ seconds
$\text{= 36}$ seconds
$\Rightarrow \text{1 }\%$ of $\text{1}$ hour $\text{= 36}$ seconds
(c). $\text{20 }\%$ of Rs$\text{2500}$
Ans: Needed to find the required percentage of the given currency Rs$\text{2500}$ i.e.,
$\text{20 }\%$ of Rs$\text{2500}$ $\text{= }\frac{\text{20}}{\text{100}}\text{ }\!\!\times\!\!\text{ 2500}$
$\text{= 20 }\!\!\times\!\!\text{ 25}$
$\text{=}$ Rs $\text{500}$
$\Rightarrow \text{20 }\%$ of Rs$\text{2500}$$\text{=}$Rs$\text{500}$
(d). $\text{75 }\%$ of $\text{1}$ kg
Ans: Needed to find the required percentage of the given quantity $\text{1}$ kg i.e.,
$\text{75 }\%$ of $\text{1}$ kg $\text{= }\frac{75}{\text{100}}\text{ }\!\!\times\!\!\text{ 1}$ kg
$\text{= 0}\text{.75}$kg
$\Rightarrow \text{75 }\%$ of $\text{1}$ kg $\text{= 0}\text{.75}$kg
5. Find the whole quantity if:
(a). $\text{5 }\%$ of it is $\text{600}$
Ans: Let the required whole quantity be $\text{x}$
Therefore, $\text{5 }\%$ of $\text{x}$ $\text{= 600}$
$\Rightarrow \text{ }\frac{\text{5}}{\text{100}}\text{ }\!\!\times\!\!\text{ x = 600}$
$\Rightarrow \text{ x = }\frac{\text{600 }\!\!\times\!\!\text{ 100}}{\text{5}}$
$\Rightarrow \text{ x = 12000}$
(b). $\text{12 }\%$ of it is Rs$\text{1080}$
Ans: Let the required whole quantity be $\text{x}$
Therefore, $\text{12 }\%$ of $\text{x}$ $\text{= Rs 1080}$
$\Rightarrow \text{ }\frac{\text{12}}{\text{100}}\text{ }\!\!\times\!\!\text{ x = 1080}$
$\Rightarrow \text{ x = }\frac{\text{1080 }\!\!\times\!\!\text{ 100}}{\text{12}}$
$\Rightarrow \text{ x = Rs 9000}$
(c). $\text{40 }\%$ of it is $\text{500}$ km
Ans: Let the required whole quantity be $\text{x}$
Therefore, $\text{40 }\%$ of $\text{x}$ $\text{= 500}$km
$\Rightarrow \text{ }\frac{\text{40}}{\text{100}}\text{ }\!\!\times\!\!\text{ x = 500}$
$\Rightarrow \text{ x = }\frac{\text{500 }\!\!\times\!\!\text{ 100}}{\text{40}}$
$\Rightarrow \text{ x = 1250}$km
(d). $\text{70 }\%$ of it is $\text{14}$ minutes
Ans: Let the required whole quantity be $\text{x}$
Therefore, $\text{70 }\%$ of $\text{x}$ $\text{= 14}$minutes
$\Rightarrow \text{ }\frac{\text{70}}{\text{100}}\text{ }\!\!\times\!\!\text{ x = 14}$
$\Rightarrow \text{ x = }\frac{\text{14 }\!\!\times\!\!\text{ 100}}{\text{70}}$
$\Rightarrow \text{ x = 20}$ minutes
(e). $\text{8 }\%$ of it is $\text{40}$ liters
Ans: Let the required whole quantity be $\text{x}$
Therefore, $\text{8 }\%$ of $\text{x}$ $\text{= 40}$liters
$\Rightarrow \text{ }\frac{\text{8}}{\text{100}}\text{ }\!\!\times\!\!\text{ x = 40}$
$\Rightarrow \text{ x = }\frac{\text{40 }\!\!\times\!\!\text{ 100}}{\text{8}}$
$\Rightarrow \text{ x = 500}$ liters
6. Convert given percents to decimal fractions and also fractions to simplest form:
(a). $\text{25 }\%$
Ans: We have given a percent $\text{25 }\%$
Fraction form$\text{= }\frac{\text{25}}{\text{100}}$
Simplest fractional form $\text{= }\frac{\text{1}}{\text{4}}$
Decimal form $\text{= 0}\text{.25}$
(b). $\text{150 }\%$
Ans: We have given a percent $\text{150 }\%$
Fraction form $\text{= }\frac{\text{150}}{\text{100}}$
Simplest fractional form $\text{= }\frac{\text{3}}{\text{2}}$
Decimal form $\text{= 1}\text{.5}$
(c). $\text{20 }\%$
Ans: We have given a percent $\text{20 }\%$
Fraction form $\text{= }\frac{\text{20}}{\text{100}}$
Simplest fractional form $\text{= }\frac{\text{1}}{\text{5}}$
Decimal form $\text{= 0}\text{.2}$
(d). $\text{5 }\%$
Ans: We have given a percent $\text{5 }\%$
Fraction form $\text{= }\frac{\text{5}}{\text{100}}$
Simplest fractional form $\text{= }\frac{\text{1}}{\text{20}}$
Decimal form $\text{= 0}\text{.05}$
7. In a city, $\text{30 }\%$ are females, $\text{40 }\%$ are males and remaining are children. What percent are children?
Ans: Let the percentage of children be $\text{x }\%$
It is given that the percentage of females and males are $\text{30 }\%$ and $\text{40 }\%$ respectively.
And, the total percentage $\text{= 100 }\%\text{ =}$ Percentage of males and Percentage of females and Percentage of children
$\Rightarrow \text{ 100 }\%\text{ = 30 }\%\text{ + 40 }\%\text{ + x }\%$
$\Rightarrow \text{ 100 }\%\text{ = 70 }\%\text{ + x }\%$
$\Rightarrow \text{ x }\%\text{ = 100 }\%\text{ - 70 }\%\text{ }$
$\Rightarrow \text{ x }\%\text{ = 30 }\%$
Thus $\text{30 }\%\text{ }$is the population of children in the city.
8. Out of $\text{15,000}$ voters in a constituency, $\text{60 }\%$ voted. Find the percentage of voters who did not vote. Can you now find out how many did not vote?
Ans: The total number of voters $\text{= 15,000}$
The percentage of people who voted $\text{= 60 }\%$
So, the percentage of people who didn’t vote $\text{= 100 }\%\text{ - 60 }\%$
$\text{= 40 }\%$
And, the number of actual candidates, who didn’t vote $=40 \%$ of $\text{15000}$
$\text{= 6000}$
Thus, $\text{6,000}$ people out of $\text{15,000}$ did not vote.
9. Meeta saves Rs $\text{400}$ from her salary. If this is $\text{10 }\%$ of her salary. What is her salary?
Ans: Let $\text{x}$ be the salary of Meeta.
Since $\text{10 }\%$ of her salary $\text{= Rs 400}$
$\Rightarrow \text{ 10 }\%\text{ of x = 400}$
$\Rightarrow \text{ 10 }\%\text{ }\!\!\times\!\!\text{ x = 400}$
$\Rightarrow \text{ }\frac{\text{10}}{\text{100}}\text{x = 400}$
$\Rightarrow \text{ x = Rs 4,000}$
Therefore, the salary of Meeta is $\text{Rs 4,000}$.
10. A local cricket team played $\text{20}$ matches in one season. It won $\text{25 }\%$ of them. How many matches did they win?
Ans: The local cricket team played $\text{20}$ matches.
They won $\text{25 }\%$ of matches out of $\text{20}$
Therefore, the number of matches the cricket team won $\text{= 25 }\%\text{ of 20}$
$\text{= }\frac{\text{25}}{\text{100}}\text{ }\!\!\times\!\!\text{ 20}$
$\text{= 5}$ matches
So, the local cricket team won $\text{5}$ matches out of $\text{20}$.
Conclusion
In Class 7 Maths Chapter 7 Exercise 7.1 provides a solid understanding of comparing quantities using ratios and percentages. Maths Class 7 Chapter 7 Exercise 7.1 helps students grasp the basics of these concepts and apply them in various contexts. By working through the problems, students build confidence in their ability to compare different quantities accurately, setting a strong foundation for more advanced topics.
Class 7 Maths Chapter 7: Exercises Breakdown
CBSE Class 7 Maths Chapter 7 Other Study Materials
Chapter-Specific NCERT Solutions for Class 7 Maths
Given below are the chapter-wise NCERT Solutions for Class 7 Maths. Go through these chapter-wise solutions to be thoroughly familiar with the concepts.
Important Related Links for NCERT Class 7 Maths
Access these essential links for NCERT Class 7 Maths, offering comprehensive solutions, study guides, and additional resources to help students master language concepts and excel in their exams.
FAQs on NCERT Solutions For Class 7 Maths Chapter 7 Comparing Quantities Exercise 7.1 - 2025-26
1. Where can I find accurate, step-by-step NCERT Solutions for Class 7 Maths Chapter 7 for the 2025-26 session?
You can find reliable and detailed NCERT Solutions for Class 7 Maths Chapter 7, Comparing Quantities, on Vedantu. These solutions are meticulously prepared by expert teachers and are fully aligned with the latest CBSE 2025-26 syllabus, providing the correct method for solving every problem in the textbook.
2. What are the main concepts covered in NCERT Class 7 Maths Chapter 7, Comparing Quantities?
Chapter 7, Comparing Quantities, primarily focuses on methods to compare different numerical values. The key concepts you will learn are:
Ratios and Percentages: Understanding equivalent ratios and converting between fractions, decimals, and percentages.
Percentage Change: Calculating percentage increase or decrease in various contexts.
Profit and Loss: Using percentages to find profit, loss, cost price (CP), and selling price (SP).
Simple Interest: Calculating interest on a principal amount over a period of time.
3. What is the correct method for finding the ratio of two quantities as per the NCERT solutions?
To find the ratio of two quantities correctly, you must follow these steps: First, ensure both quantities are in the same unit (e.g., convert metres to centimetres or paise to rupees). Next, write the two quantities as a fraction. Finally, simplify the fraction to its lowest terms. For example, the ratio of 50 paise to ₹5 is found by converting ₹5 to 500 paise, giving the ratio 50:500, which simplifies to 1:10.
4. How do you solve problems involving the conversion of a ratio to a percentage?
The step-by-step method to convert a ratio to a percentage is straightforward. First, write the ratio as a fraction. For a ratio a:b, the fraction is a/b. Then, multiply this fraction by 100 and add the percentage symbol (%). For example, to convert the ratio 2:5 to a percentage, you calculate (2/5) × 100, which equals 40%.
5. What are the key formulas used in Chapter 7 for calculating profit, loss, and simple interest?
The NCERT solutions for this chapter use several important formulas:
Profit = Selling Price (SP) - Cost Price (CP)
Loss = Cost Price (CP) - Selling Price (SP)
Profit Percentage = (Profit / CP) × 100
Loss Percentage = (Loss / CP) × 100
Simple Interest (SI) = (Principal × Rate × Time) / 100
6. Why is it crucial to ensure quantities are in the same units before comparing them as a ratio?
It is crucial because a ratio is a comparison of magnitudes, and this comparison is only meaningful if the units are identical. For instance, comparing 2 kg to 500 grams directly is misleading. By converting 2 kg to 2000 grams, you can form a correct ratio of 2000:500, or 4:1. This ensures you are comparing 'like with like', which is the fundamental principle of forming a valid mathematical ratio.
7. How do the NCERT Solutions for Chapter 7 help in solving complex word problems on profit and loss?
The NCERT Solutions help by breaking down complex word problems into simple, understandable steps. They show you how to:
Identify the Cost Price (CP) and Selling Price (SP) from the problem statement.
Choose the correct formula based on whether it's a profit or a loss scenario.
Substitute the values correctly and perform the calculation accurately.
This step-wise approach builds a strong problem-solving methodology, reducing errors in exams.
8. What is the fundamental difference between a ratio and a fraction in the context of this chapter?
While mathematically similar, their application differs. A fraction typically represents a part of a whole (e.g., 3/4 of a cake). A ratio, on the other hand, compares two distinct quantities (e.g., the ratio of apples to oranges is 3:4). The key difference is the context: a fraction is about a single entity, while a ratio compares two separate entities.
9. How can the concept of percentages from this chapter be applied to real-world scenarios like calculating discounts?
Percentages are extremely useful in real life. For example, to calculate a discount, you convert the percentage to a fraction or decimal and multiply it by the original price. If a shirt costs ₹800 and has a 20% discount, the discount amount is (20/100) × 800 = ₹160. The final selling price would be ₹800 - ₹160 = ₹640. This same principle applies to calculating taxes, tips, and interest.
10. What is a common mistake students make when calculating Simple Interest, and how do NCERT solutions prevent it?
A common mistake is using the 'Time' variable incorrectly, especially when it's given in months or days. The rate of interest is usually annual, so the time must also be in years. For example, if the time is 6 months, it must be written as 6/12 or 0.5 years in the formula. NCERT solutions explicitly show this conversion step, reinforcing the correct method and helping students avoid losing marks for this common oversight.
