# NCERT Class 7 Maths Chapter 7 Comparing Quantities Notes and Solutions PDF

NCERT Class 7 Maths Chapter 7, Comparing Quantities teaches the concept of percentages. The chapter emphasizes the use of percentages in carrying out comparisons of different kinds. In the later part of this chapter, students will also learn the conversion of percentages into fractions and decimals, the concepts of profit and loss, cost price, and selling price. Lastly, the chapter concludes with the important lessons of the calculation of Simple Interest on the sum borrowed. Let us now have a look at the NCERT Class 7 Maths Chapter 7 Comparing Quantities Notes and Solutions (PDF).

## NCERT Class 7 Maths Chapter 7 Notes – PDF Available

Check the topic-wise notes for NCERT Maths Class 7 – Chapter 7 below. You can also download the PDF of the notes and take a printout to study later when you need quick revision before going to the e𝑥am hall.

Top 10 Short Maths Tricks for Complex Problems

### Topic 1: What are Percentages?

Percentages are numerators of fractions with denominator 100 and are used in comparing results.

Maths Books for Competitive E𝑥ams

### Topic 2: Percentage When Denominator is not 100 (Converting Fractional Numbers to Percentage)

How do we calculate the percentage of an item if the total number of items does not add up to 100? In such cases, we need to convert the fraction to an equivalent fraction with a denominator of 100.

For example, let us see the conversion of fraction 8/20 into percentage by two methods, you can use any of these methods in your calculations.

Method 1:

Method 2:

Both these methods are simple and effective in determining percentages from fractions.

1. Cost Price: The buying price of any item is known as its cost price (CP).
2. Selling Price: The price at which you sell is known as the selling price (SP).

### Topic 4: Profit or Loss

The profit or loss on a product is calculated only on its cost price.

Maths Formulas for Class 10

### Topic 5: Charge Given on Borrowed Money or Simple Interest

1. Sum or Principal: The money you borrow is known as the sum borrowed or principal.
2. Interest: The borrowed money would be used by the borrower for some time before it is returned. To keep this money for some time, the borrower has to pay some extra money to the bank. This is known as Interest.
3. Rate of Interest: Interest is generally given in percent for the period of the desired number of years. This percentage is referred to as the Rate of Interest.
4. Amount: The amount you have to pay at the end of the year can be calculated by adding the sum borrowed and the interest.

∴ Amount = Principal + Interest

1. Simple Interest: The way of calculating interest where the principal is not changed is known as simple interest.

### Topic 6: Calculation of Interest for 1 Year

The amount of interest (I) or Simple Interest to be paid for 1 year on a borrowed sum of ₹ P at an interest of R% can be calculated by the following formula.

Where I = Interest (extra money than the borrowed sum) to be paid yearly on the borrowed sum

P = borrowed sum

R = Rate of Interest

### Topic 6: Calculation of Interest for Multiple Years

If the amount is borrowed for more than one year, the interest is calculated for the period the money is kept for.

The amount of interest (I) or Simple Interest to be paid when the sum borrowed (₹ P) at an interest of R% is kept for more than 1 year can be calculated by the following formula.

Where I = Interest (extra money than the borrowed sum) to be paid yearly on the borrowed sum

P = borrowed sum

R = Rate of Interest

T = The number of years for which the borrowed sum is kept by the borrower

∴ Amount to be paid after T years can be calculated by:

Maths for Competitive E𝑥ams

## Chapter 7, Comparing Quantities Solutions – PDF Available!

Below we have provided solutions for NCERT Class 7 Maths Chapter 7, Comparing Quantities. Go through for answers to some important questions.

Courses and Career Options in Commerce Without Maths in 2023

### E𝑥ercise 7.1 Solutions

Q 1. Convert the given fractional numbers to per cents.

1. ⅛
2. 2/7

Solutions. The answers are given below.

1. To calculate the percentage of the given fraction, let us multiply the numerator and denominator by 100.

∴ ⅛ in percentage is 12.5%.

1. To calculate the percentage of the given fraction, let us multiply the numerator and denominator by 100.

∴ ⅛ in percentage is 28(4/7)% or .

SAT Maths Subject Test

Q 2. Find:

1. 15% of 250
2. 1% of 1 hour
3. 75% of 1 kg

Solutions. In class 6, we have understood that “of” symbolizes the multiplication function (or parts of). The answers are given below.

1. We can write the given expression as:

∴ 15% of 250 is 37.5.

1. We know that 1 hour = 60 minutes and 1 minute = 60 seconds

Thus, 1 minute = 60 × 60 seconds = 3600 seconds

Let us now determine 1% of 1 hour or 3600 seconds below.

∴ 1% of 1 hour is 36 seconds.

1. We know that 1 kg = 1000 g.

So, we can write the given expression as:

∴ 75% of 1 kg is 750 g.

NCERT Class 8 Maths Syllabus

Q 3. Find the whole quantity if

1. 5% of it is 600.
2. 40% of it is 500 km.
3. 70% of it is 14 minutes

Solutions. The whole quantities of the given expressions are deduced below.

1. Let us assume the whole quantity to be 𝑥. So, an equation can be formed as:

⇒ 5% of 𝑥 = 600

⇒ 5/100 × 𝑥 = 600

⇒ 𝑥 = 600 × 100/5 = 12000

⇒ 𝑥 = 12000

∴ The whole quantity is 12,000.

1. Let us assume the whole quantity to be 𝑥. So, an equation can be formed as:

⇒ 40% of 𝑥 = 500 km

⇒ 40/100 × 𝑥 = 500

⇒ 𝑥 = 500 × 100/40 = 1250

⇒ 𝑥 = 1250

∴ The whole quantity is 1250 km.

1. Let us assume the whole quantity to be 𝑥. So, an equation can be formed as:

⇒ 70% of 𝑥 = 14 min

⇒ 70/100 × 𝑥 = 14

⇒ 𝑥 = 14 × 100/70 = 20

⇒ 𝑥 = 20

∴ The whole quantity is 20 minutes.

Career after BSc Maths

### E𝑥ercise 7.2 Solutions

Q 1. Amina buys a book for ₹ 275 and sells it at a loss of 15%. How much does she sell it for?

Solutions. The cost price (CP) of the book is ₹ 275 and Amina sold the book at a loss of 15%. Therefore, the selling price (SP) of the book can be calculated as follows:

SP = CP – (15% of CP)

Now, 15% of CP = 15/100 × 275 = ₹ 41.25

∴ SP = ₹ 275 – ₹ 41.25 = ₹ 233.75 = ₹ 234

Hence, Amina sold the book for ₹ 234 (approximately).

Q 2. What rate gives ₹ 280 as interest on a sum of ₹ 56,000 in 2 years?

Solutions: From the question, we know that:

I = ₹ 280

P = ₹ 56,000

T = 2 years

We have to determine “R” for the given problem. We know that simple interest for multiple years is calculated as:

∴ The rate of interest for 2 years is 0.25%.

## FAQs

Q.1. What is simple interest (SI)?

Ans: The way of calculating interest where the principal or sum is not changed is known as simple interest.

Q.2. What is a rate of interest?

Ans: Interest is generally given in percent for the period of the desired number of years. This percentage is referred to as the Rate of Interest.

Q.3. What is the difference between the cost price (CP) and the selling price (SP)?

Ans: The buying price of any item is known as its cost price (CP). Whereas, the price at which you sell it is known as the selling price (SP).

Check out more interesting blogs below.

This was all about NCERT Class 7 Maths Chapter 7, Comparing Quantities in which we studied how to draw comparisons using percentages. Download the NCERT Class 7 Maths Chapter 7 Notes and Solutions PDF to ace your e𝑥am preparations. Follow the CBSE Class 7 Maths Solutions and Notes for more such chapter notes and important questions and answers for preparation for CBSE Class 7 Maths.