Class 8 Maths Ex. 7.1 Comparing Quantities: NCERT Solutions

In the Exercise 7.1 of Comparing Quantities in NCERT book we will be solving questions on Ratios and Percentages. This is something we have already solved in class 7th. Lets have a look at some basics to refresh our knowledge.

Ratios

Definition: A ratio represents the relationship between two numbers, showing how many times one value contains the other.

Example of Ratios:

Consider a bag containing 6 apples and 4 oranges. The ratio of apples to oranges is 6:4, which simplifies to 3:2. This means for every 3 apples, there are 2 oranges.

Percentages

Definition: A percentage is a part of a whole expressed in hundredths.

Example of Percentages:

If there are 50 students in a class and 15 of them are boys, then the percentage of boys is calculated as (15/50) × 100 = 30%. This means 30% of the class is boys.

NCERT Solutions for Class 8 Maths Exercise 7.1 Chapter 7 Comparing Quantities

Question 1. Find the ratio of the following:

(a) Speed of a cycle 15 km per hour to the speed of scooter 30 km per hour. (b) 5 m to 10 km (c) 50 paise to ₹ 5

Solution

(a) Speed of a cycle 15 km per hour to the speed of scooter 30 km per hour.
Given:
Speed of the cycle = 15 km/h
Speed of the scooter = 30 km/h

Ratio of speed of the cycle vs speed of the scooter = (15 km/h)/30 km/h
= 15/30 = 1/2 = 1 : 2

(b) 5 m to 10 km
Given:
Distance in meters = 5 m
Distance in kilometers = 10 km

First, convert kilometers to meters: 10 km = 10,000 m

Ratio of 5 m to 10,000 m = 5/10000 = 1/2000 = 1 : 2000

(c) 50 paise to ₹ 5
Given:
Amount in paise = 50 paise
Amount in rupees = ₹ 5

First, convert rupees to paise: ₹ 5 = 500 paise

Ratio of 50 paise to 500 paise = 50/500 = 1/10 = 1 : 10

Question 2. Convert the following ratios to percentages:

(a) 3 : 4 (b) 2 : 3

Solution

(a) The ratio 3:4 as a percentage is (3/4) × 100% = 75%.

(b) The ratio 2:3 as a percentage is (2/3) × 100% ≈ 66.67%.

Question 3. 72% of 25 students are interested in mathematics. How many are not interested in mathematics?

Solution

Given:
Total number of students = 25
Percentage interested in mathematics = 72%

Number of students interested in mathematics = (72/100) × 25 = 18

Therefore, number of students not interested in mathematics = Total students – Students interested in mathematics = 25 – 18 = 7

7 students are not interested in mathematics.

Question 4. A football team won 10 matches out of the total number of matches they played. If their win percentage was 40, then how many matches did they play in all?

Solution

Given:
Number of matches won = 10
Win percentage = 40%

Let the total number of matches played be x.

According to the problem, 40% of x = 10
=> (40/100) × x = 10
=> x = 10 × 100/40
=> x = 25

The team played 25 matches in all.

Question 5. If Chameli had ₹ 600 left after spending 75% of her money, how much did she have in the beginning?

Solution

Given:
Amount left = ₹ 600
Percentage of money spent = 75%

Let the original amount be x.

Amount spent = 75% of x = (75/100) × x
Amount left = 25% of x = (25/100) × x

According to the problem, (25/100) × x = 600
=> x = 600 × 100/25
=> x = ₹ 2400

Chameli had ₹ 2400 in the beginning.

Question 6. If 60% of people in a city like cricket, 30% like football, and the remaining like other games, then what percent of the people like other games? If the total number of people is 50 lakh, find the exact number who like each type of game.

Solution

Given:
Total number of people = 50 lakh
Percentage liking cricket = 60%
Percentage liking football = 30%

Percentage liking other games = 100% – (Percentage liking cricket + Percentage liking football)
= 100% – (60% + 30%)
= 100% – 90%
= 10%

Number of people liking cricket = (60/100) × 50 lakh = 30 lakh
Number of people liking football = (30/100) × 50 lakh = 15 lakh
Number of people liking other games = (10/100) × 50 lakh = 5 lakh

30 lakh people like cricket, 15 lakh people like football, and 5 lakh people like other games.

Practice Worksheet with Challenging Questions For Class 8 Ex. 7.1 Comparing Quantities

Questions

1. Find the selling price of a book originally priced at ₹500 after a discount of 10%.
2. A laptop is sold at ₹45,000 after a discount of 10%. Find the original price.
3. Calculate the simple interest on ₹20,000 for 2 years at an annual interest rate of 5%.
4. The price of a car depreciates by 15% each year. Find its value after 2 years if the current price is ₹1,00,000.
5. Find the selling price of a shirt marked at ₹800 with a discount rate of 15%.
6. If a sum of ₹30,000 is deposited in a bank at an interest rate of 6% per annum, find the interest after 1 year.
7. A refrigerator is sold at ₹18,000 after a 10% discount. Find the original price.
8. Calculate the compound interest on ₹5000 for 3 years at an annual interest rate of 4%, compounded annually.
9. The population of a town increases by 5% per year. If the current population is 20,000, what will it be after 3 years?
10. A book’s price increases by 20% annually. If the current price is ₹250, what will be the price after 2 years?
11. Find the final amount after applying a 12% VAT on an item priced at ₹2000.
12. Calculate the sale price of a bicycle after a discount of 30% on the marked price of ₹5000.
13. A sum of ₹10,000 is invested in a savings account at 8% per annum. Find the interest after 2 years.
14. If the price of gold increases by 10% annually, what will be the price of gold after one year, originally priced at ₹30,000?
15. The price of a smartphone, including 18% GST, is ₹35,640. Find the price before GST.

Answers

1. Selling price of the book: ₹450.
2. Original price of the laptop: ₹50,000.
3. Simple interest: ₹2000.
4. Value of the car after 2 years: ₹72,250.
5. Selling price of the shirt: ₹680.
6. Interest earned: ₹1800.
7. Original price of the refrigerator: ₹20,000.
8. Compound interest: ₹624.32.
9. Population after 3 years: approximately 23,150.
10. Price of the book after 2 years: ₹360.
11. Final amount including VAT: ₹2240.
12. Sale price of the bicycle: ₹3500.
13. Interest earned in 2 years: ₹1600.
14. Price of gold after one year: ₹33,000.
15. Price of the smartphone before GST: ₹30,200.