# NCERT Solutions for Class 7 Maths Chapter 8 Comparing Quantities

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NCERT Solutions for Class 7 Maths Chapter 8 Comparing Quantities: In our daily life we compare many things, Like his mark is twice of my mark, the bottle only filled up to two-thirds of its height, My mark increased by 10 percent compared to the last test, shopkeeper got a profit of 2 percentage by selling an item, etc. In NCERT Solutions for Class 7 Maths Chapter 8, we will study how to compare quantities using ratios and percentage and the concept of profit, loss and simple interest. All these concepts are useful in our daily life and these are the basics for calculations in our life. We must be through with this chapter of NCERT Solutions for Class 7 Maths. The concept studied here will be used in NCERT Solutions of 8,9 and 10th class and also in our higher studies.

Ratio: Ratio is used to compare quantities. The ratio tells how much is a quantity is compared to others. To find the ratio of two quantities their unit must be the same. That is if we have to find the ratio of 500meter and 1 Km first we have to convert it to the same unit. 1Km=1000m. Now the ratio is 500:1000 or 1:2. Using the concept of ratios we can solve many interesting problems.

Let's take an example from NCERT Solutions for Class 7 Maths Chapter 8 Comparing Quantities, exercise 8.1 question 2

Q)  In a computer lab, there are 3 computers for every 6 students. How many computers will be needed for 24 students?

Solution: 3 computers for 6 students which mean number of computers: number of students = 3:6=1:2, that is

$\\\frac{number \ of\ computers}{number \ of students}=\frac{1}{2}\\number\ of\ computers=\frac{1}{2}number \ of students\\number \ of\ computers=\frac{1}{2} \times 24=12$

That is 24 students requires 12 computers.

Percentage: Percentages are numerators of fractions with denominator as 100. The percentage is represented by '%'. 1% means 1 out of 100. That is 1/100= 0.01. Let's see an example of how to calculate the percentage

Ex 1) Out of 30 students in class 18 are boys. What is the percentage of girls in the class?

Solution:

$\\30\ students=100\%\\\ 1\ student=\frac{100\%}{30}\\18\ students=\frac{18}{30}\times100\%=\frac{6}{10}\times100\%=60\%$

60% of students are boys, so the percentage of girls= 100-60=40%. That is 30-18=12 are girls.

Suppose in this class 30% sings. Then how many students will sing?

Solution:

$\\100\%=30\ students\\\ 1\%=\frac{30}{100}\ students\\ 30\%=\frac{30}{100}\times30=9$

So 9 students are singers

The main and subheadings of NCERT Solutions for Class 7 Maths Chapter 8 Comparing Quantities are listed below:

8.1 Introduction

8.2 Equivalent Ratios

8.3 Percentage – Another Way Of Comparing Quantities

8.3.1 Meaning Of Percentage

8.3.2 Converting Fractional Numbers To Percentage

8.3.3 Converting Decimals To Percentage

8.3.4 Converting Percentages To Fractions Or Decimals

8.3.5 Fun With Estimation

8.4 Use Of Percentages

8.4.1 Interpreting Percentages

8.4.2 Converting Percentages To “How Many”

8.4.3 Ratios To Percents

8.4.4 Increase Or Decrease As a percent

8.5 Prices Related To An Item Or Buying And Selling

8.5.1 Profit Or Loss As A Percentage

8.6 Charge Given On Borrowed Money Or Simple Interest

8.6.1 Interest For Multiple Years

The other two main topics of NCERT Solutions for Class 7 Maths Chapter 8  are Profit and Loss percentage and Simple interest. If selling price (SP) is > cost price (CP) then there is a profit P= SP-CP.  If selling price (SP) is < cost price (CP) then there is a loss L= CP-SP.

$profit\ per\ cent=\frac{SP-CP}{CP}\times100\%=\frac{profit}{CP}\times100\%$

$loss\ per\ cent=\frac{CP-SP}{CP}\times100\%=\frac{loss}{CP}\times100\%$

Simple interest: If we deposit 100 rupees for the interest of 10% for a year then we will get 100+10% of 100=100+10=110 rupees after a year. Here 100 rupees is known as the principal or sum (P), 10% is the rate percent per annum (R), Then the interest we are getting (I) after 1 year is (If we are borrowing money then the interest is to be paid)

$I=\frac{PR}{100}=\frac{100\times10}{100}=10$

The amount (A) we receive =  P+I=100+10=110

Suppose if we are borrowing or taking a loan for more than one year (say T years) then the interest to be paid after T years is

$I=\frac{PRT}{100}$

For example, if we take a loan of 10000 rupees for 4% interest the amount to be paid after 3 years= P+I

Where

$I=\frac{PRT}{100}=\frac{10000\times4\times3}{100}=1200$

Therefor amount to be paid A=P+I=10000+1200=11200 rupees

There are such many examples in the NCERT book and solving all the questions are mandatory to score well in the exam and to be familiar with the concepts.

## NCERT Solutions for Class 7 Maths - Chapter-wise

 Chapter No. Chapter Name Chapter 1 Integers Chapter 2 Fractions and Decimals Chapter 3 Data Handling Chapter 4 Simple Equations Chapter 5 Lines and Angles Chapter 6 The Triangle and its Properties Chapter 7 Congruence of Triangles Chapter 9 Rational Numbers Chapter 10 Practical Geometry Chapter 11 Perimeter and Area Chapter 12 Algebraic Expressions Chapter 13 Exponents and Powers Chapter 14 Symmetry