Class 8 Maths Part 2 Chapter 1 – Fractions in Disguise | NCERT Ganita Prakash Notes & Book Solutions
Class 8 Maths Part 2 Chapter 1 – Fractions in Disguise from NCERT Ganita Prakash with easy Notes and complete Book Solutions. Get simple explanations, important concepts, questions and answers, and revision material for effective learning, practice and exam preparation.
Class 8 Maths Fractions in Disguise – Easy Notes, Concepts and Solutions
Fractions in Disguise
Class 8 Mathematics – Ganita Prakash Part-II
Easy Notes • Concepts • Book Solutions • Practice
Chapter at a Glance
Percentage means “per hundred”.
The symbol % is read as “per cent”. The phrase comes from “per centum”, meaning “by the hundred”.
For example, 25% means 25 out of every 100.
25% = 25/100 = 1/4
Therefore, percentages are simply fractions whose denominator is 100.
25%
25 out of 100 = 25%
Main topics in this chapter
Fractions as percentages
Percentage of a quantity
Fractions, decimals and percentages
Percentages greater than 100
Comparing proportions
Percentage increase and decrease
Profit and loss
Discount and GST
Growth and compounding
Decline and depreciation
Tricky percentages
1.1 Fractions as Percentages
To convert a fraction into a percentage:
Percentage = Fraction × 100
Example
Express 3/4 as a percentage.
1. Multiply by 100.
3/4 × 100 = 75
2. Therefore:
3/4 = 75%
Easy trick: Try to change the denominator into 100.
Another example
2/5 = 2/5 × 100 = 40%
2/5 = 40%
Percentage into Fraction
A percentage can be written over 100.
24% = 24/100 = 12/50 = 6/25
Figure it Out – Fractions as Percentages
1. Express the following fractions as percentages.
2. Nandini has 25 marbles, of which 15 are white. What percentage of her marbles are white?
(i) 10% (ii) 15% (iii) 25% (iv) 60% (v) 40% (vi) None of these
Percentage = 15/25 × 100
= 3/5 × 100 = 60%
Answer: (iv) 60%
3. In a school, 15 of the 80 students come to school by walking. What percentage of the students come by walking?
Percentage = 15/80 × 100
= 18.75%
Answer: 18.75%
4. A group of friends is participating in a long-distance run. The positions of each of them after 15 minutes are shown in the following picture. Match (among the given options) what percentage of the race each of them has approximately completed.
Options: 55%, 20%, 38%, 72%, 84%, 93%
From the positions shown in the textbook figure:
Runner
Approximate completion
A
38%
B
55%
C
72%
D
93%
5. Pairs of quantities are shown below. Identify and write appropriate symbols ‘>’, ‘<’, ‘=’ in the blanks. Try to do it without calculations.
Mental Maths Tip:
25% means one-fourth.
50% means one-half.
10% means one-tenth.
5% means half of 10%.
Useful relationships
Percentage
Easy form
50%
1/2
25%
1/4
75%
3/4
10%
1/10
20%
1/5
5%
1/20
1%
1/100
Figure it Out – Percentage of Some Quantity
Estimate first before making any computations to solve the following questions. Try different methods including mental computations.
1. Find the missing numbers. The first problem has been worked out.
2. Find the value of the following and also draw their bar models.
(i) 25% of 160
(ii) 16% of 250
(iii) 62% of 360
(iv) 140% of 40
(v) 1% of 1 hour
(vi) 7% of 10 kg
3. Surya made 60 ml of deep orange paint, how much red paint did he use if red paint made up 3/4 of the deep orange paint?
Red paint = 3/4 × 60
= 45 ml
Answer: 45 ml of red paint.
4. Pairs of quantities are shown below. Identify and write appropriate symbols ‘>’, ‘<’, ‘=’ in the boxes. Visualising or estimating can help. Compute only if necessary or for verification.
(i) 50% of 510 ____ 50% of 515
(ii) 37% of 148 ____ 73% of 148
(iii) 29% of 43 ____ 92% of 110
(iv) 30% of 40 ____ 40% of 50
(v) 45% of 200 ____ 10% of 490
(vi) 30% of 80 ____ 24% of 64
(i) <
(ii) <
(iii) <
(iv) Both are 12 and 20 respectively, so <
(v) 90 > 49, so >
(vi) 24 > 15.36, so >
5. Fill in the blanks appropriately:
(i) 30% of k is 70, 60% of k is _____, 90% of k is _____, 120% of k is ______.
(ii) 100% of m is 215, 10% of m is _____, 1% of m is ______, 6% of m is ______.
(iii) 90% of n is 270, 9% of n is ______, 18% of n is _____, 100% of n is ______.
(iv) Make 2 more such questions and challenge your peers.
(i)
30% of k = 70
k = 70 × 100/30 = 700/3
60% = 140
90% = 210
120% = 280
(ii)
100% of m = 215
10% = 21.5
1% = 2.15
6% = 12.9
(iii)
90% of n = 270
100% of n = 300
9% = 27
18% = 54
100% = 300
6. Fill in the blanks:
(i) 3 is ____ % of 300.
(ii) _____ is 40% of 4.
(iii) 40 is 80% of _____.
(i) 3/300 × 100 = 1%
(ii) 40/100 × 4 = 1.6
(iii) 40 = 80/100 × x, so x = 50
7. Is 10% of a day longer than 1% of a week? Create such questions and challenge your peers.
10% of one day = 10% × 24 hours = 2.4 hours.
1% of one week = 1% × 7 days = 0.07 day = 1.68 hours.
Yes, 10% of a day is longer.
8. Mariam’s farm has a peculiar bull. One day she gave the bull 2 units of fodder and the bull ate 1 unit. The next day, she gave the bull 3 units of fodder and the bull ate 2 units. The day after, she gave the bull 4 units and the bull ate 3 units. This continued, and on the 99th day she gave the bull 100 units and the bull ate 99 units. Represent these quantities as percentages. This task can be distributed among the class. What do you observe?
Day 1: 1/2 × 100 = 50%
Day 2: 2/3 × 100 = 66.67%
Day 3: 3/4 × 100 = 75%
The pattern continues:
Day n: n/(n+1) × 100%.
On the 99th day:
99/100 × 100 = 99%.
Observation: The percentage keeps getting closer to 100%, but it never reaches 100%.
9. Workers in a coffee plantation take 18 days to pick coffee berries in 20% of the plantation. How many days will they take to complete the picking work for the entire plantation, assuming the rate of work stays the same? Why is this assumption necessary?
20% takes 18 days.
100% is five times 20%.
18 × 5 = 90 days.
The assumption is necessary because the calculation assumes that the workers continue working at the same rate throughout the plantation.
10. The badminton coach has planned the training sessions such that the ratio of warm up : play : cool down is 10% : 80% : 10%. If he wants to conduct a training of 90 minutes. How long should each activity be done?
Warm up = 10% of 90 = 9 minutes
Play = 80% of 90 = 72 minutes
Cool down = 10% of 90 = 9 minutes
11. An estimated 90% of the world’s population lives in the Northern Hemisphere. Find the (approximate) number of people living in the Northern Hemisphere based on this year’s worldwide population.
Using the chapter’s approximate world population of 8.2 billion:
90% of 8.2 billion = 0.90 × 8.2
= 7.38 billion approximately.
12. A recipe for the dish, halwa, for 4 people has the following ingredients in the given proportions — Rava: 40%, Sugar: 40%, and Ghee: 20%.
(i) If you want to make halwa for 8 people, what is the proportion of each of the above ingredients?
(ii) If the total weight of the ingredients is 2 kg, how much rava, sugar and ghee are present?
(i) The proportions remain the same:
Rava = 40%, Sugar = 40%, Ghee = 20%
(ii)
Rava = 40% of 2 kg = 0.8 kg
Sugar = 40% of 2 kg = 0.8 kg
Ghee = 20% of 2 kg = 0.4 kg
1.3 Using Percentages to Compare Proportions
When two quantities have different totals, simply comparing their marks or amounts may not be fair.
Convert both quantities into percentages before comparing them.
Example
Eesha scored 42 marks out of 50 in English and 70 marks out of 80 in Science.
English = 42/50 × 100 = 84%
Science = 70/80 × 100 = 87.5%
Therefore, the Science score is higher when compared as percentages.
Know Your Contents
For the DEF product:
Ingredient
Amount
Percentage
Sugar
99 g
66%
Milk Solids
30 g
20%
Badam Powder
12 g
8%
Food Chemicals
9 g
6%
For the Zachi product:
Ingredient
Amount
Percentage
Sugar
272 g
68%
Milk Solids
64 g
16%
Badam Powder
40 g
10%
Food Chemicals
24 g
6%
For both products, the ingredient percentages add up to 100%.
Percentage Increase or Decrease
Percentage increase =
(amount of increase ÷ original amount) × 100
Percentage decrease =
(amount of decrease ÷ original amount) × 100
Example
Price increases from ₹30 to ₹42.
Increase = ₹42 − ₹30 = ₹12
Percentage increase = 12/30 × 100 = 40%
Example of decrease
Footfall decreases from 160 to 100.
Decrease = 60
Percentage decrease = 60/160 × 100 = 37.5%
Profit and Loss
Profit = Selling Price − Cost Price
Loss = Cost Price − Selling Price
Profit % = (Profit ÷ Cost Price) × 100
Loss % = (Loss ÷ Cost Price) × 100
Important: Profit or loss percentage is normally calculated with respect to the cost price.
Cost Price, Marked Price and Selling Price
CP: Cost Price – price paid to buy the item.
MP: Marked Price – price written/quoted for the item.
SP: Selling Price – price actually paid by the customer.
Figure it Out – Profit, Loss, Discount and Increase
1. If a shopkeeper buys a geometry box for ₹75 and sells it for ₹110, what is his profit margin with respect to the cost?
Profit = 110 − 75 = ₹35
Profit % = 35/75 × 100
= 46.67% approximately.
2. I am a carpenter and I make chairs. The cost of materials for a chair is ₹475 and I want to have a profit margin of 50%. At what price should I sell a chair?
Profit = 50% of ₹475
= 0.5 × 475 = ₹237.50
Selling price = 475 + 237.50
= ₹712.50
3. The total sales of a company (also called revenue) was ₹2.5 crore last year. They had a healthy profit margin of 25%. What was the total expenditure (costs) of the company last year?
Profit = 25% of revenue.
Therefore, expenditure = 100% − 25% = 75% of revenue.
75% of ₹2.5 crore = ₹1.875 crore.
Answer: ₹1.875 crore.
4. A clothing shop offers a 25% discount on all shirts. If the original price of a shirt is ₹300, how much will Anwar have to pay to buy this shirt?
Discount = 25% of ₹300 = ₹75
Selling price = ₹300 − ₹75
= ₹225
5. The petrol price in 2015 was ₹60 and ₹100 in 2025. What is the percentage increase in the price of petrol?
3. Samson bought a car for ₹4,40,000 after getting a 15% discount from the car dealer. What was the original price of the car?
After a 15% discount, the customer pays 85% of the original price.
85% of original price = ₹4,40,000
Original price = 4,40,000 ÷ 0.85
≈ ₹5,17,647.06
4. 1600 people voted in an election and the winner got 500 votes. What percent of the total votes did the winner get? Can you guess the minimum number of candidates who stood for the election?
Percentage = 500/1600 × 100
= 31.25%
For the minimum number of candidates, there must be enough other candidates to receive the remaining 1100 votes without any one of them getting 500 or more.
With 3 candidates total, the remaining 1100 votes cannot be divided between two candidates with both getting less than 500.
With 4 candidates total, it is possible.
Minimum number of candidates = 4.
5. The price of 1 kg of rice was ₹38 in 2024. It is ₹42 in 2025. What is the rate of inflation? (Inflation is the percentage increase in prices.)
Increase = ₹42 − ₹38 = ₹4
Percentage increase = 4/38 × 100
≈ 10.53%
6. A number increased by 20% becomes 90. What is the number?
After a 20% increase, the new number is 120% of the original.
120% of number = 90
Number = 90 ÷ 1.2
= 75
7. A milkman sold two buffaloes for ₹80,000 each. On one of them, he made a profit of 5% and on the other a loss of 10%. Find his overall profit or loss.
First buffalo:
Selling price = ₹80,000
At 5% profit, CP = 80,000/1.05 ≈ ₹76,190.48
Second buffalo:
At 10% loss, SP = 90% of CP.
CP = 80,000/0.90 ≈ ₹88,888.89
Total CP ≈ ₹1,65,079.37
Total SP = ₹1,60,000
Loss ≈ ₹5,079.37
Loss percentage ≈ 5079.37/165079.37 × 100
Overall loss ≈ 3.08%
8. The population of elephants in a national park increased by 5% in the last decade. If the population of the elephants last decade is p, the population now is
(i) p × 0.5
(ii) p × 0.05
(iii) p × 1.5
(iv) p × 1.05
(v) p + 1.50
A 5% increase means 105% of the original.
Answer: (iv) p × 1.05
9. Which of the following statement(s) mean the same as — “The demand for cameras has fallen by 85% in the last decade”?
(i) The demand now is 85% of the demand a decade ago.
(ii) The demand a decade ago was 85% of the demand now.
(iii) The demand now is 15% of the demand a decade ago.
(iv) The demand a decade ago was 15% of the demand now.
(v) The demand a decade ago was 185% of the demand now.
(vi) The demand now is 185% of the demand a decade ago.
A fall of 85% means 100% − 85% = 15% remains.
Answer: (iii)
Growth and Compounding
Simple/no compounding: The original principal remains the same for each term.
Compounding: The interest is added back to the principal, so the next interest is calculated on a larger amount.
Without compounding:
A = P(1 + rt)
With annual compounding:
A = P(1 + r)t
Here r is written as a decimal. For example, 10% = 0.10.
Example: ₹6000 at 10% for 3 years
Year
Beginning
Interest
Ending
1
₹6000
₹600
₹6600
2
₹6600
₹660
₹7260
3
₹7260
₹726
₹7986
With compounding, final amount = ₹7986.
Figure it Out – Growth and Compounding
1. Bank of Yahapur offers an interest of 10% p.a. Compare how much one gets if they deposit ₹20,000 for a period of 2 years with compounding and without compounding annually.
Without compounding:
Interest = 20,000 × 0.10 × 2 = ₹4,000
Amount = ₹24,000
With compounding:
A = 20,000 × 1.1 × 1.1
= ₹24,200
2. Bank of Wahapur offers an interest of 5% p.a. Compare how much one gets if one deposits ₹20,000 for a period of 4 years with compounding and without compounding annually.
Without compounding:
Interest = 20,000 × 0.05 × 4 = ₹4,000
Amount = ₹24,000
With compounding:
A = 20,000 × (1.05)4
= ₹24,310.13 approximately.
3. Do you observe anything interesting in the solutions of the two questions above? Share and discuss.
In both cases, the compounded amount is greater than the amount without compounding.
The reason is that with compounding, interest is added to the principal and earns further interest.
4. Jasmine invests amount ‘p’ for 4 years at an interest of 6% p.a. Which of the following expression(s) describe the total amount she will get after 4 years when compounding is not done?
(i) p × 6 × 4
(ii) p × 0.6 × 4
(iii) p × 0.6/100 × 4
(iv) p × 0.06/100 × 4
(v) p × 1.6 × 4
(vi) p × 1.06 × 4
(vii) p + (p × 0.06 × 4)
Without compounding:
Amount = p + interest
Interest = p × 0.06 × 4
Correct expression: (vii) p + (p × 0.06 × 4)
5. The post office offers an interest of 7% p.a. How much interest would one get if one invests ₹50,000 for 3 years without compounding? How much more would one get if it was compounded?
Without compounding:
Interest = 50,000 × 0.07 × 3 = ₹10,500
With compounding:
Amount = 50,000 × (1.07)3
≈ ₹61,252.15
Compound interest ≈ ₹11,252.15
Extra interest = 11,252.15 − 10,500
= ₹752.15 approximately.
6. Giridhar borrows a loan of ₹12,500 at 12% per annum for 3 years without compounding and Raghava borrows the same amount for the same time period at 10% per annum, compounded annually. Who pays more interest and by how much?
7. Consider an amount ₹1000. If this grows at 10% p.a., how long will it take to double when compounding is done vs. when compounding is not done? Is compounding an example of exponential growth and not-compounding an example of linear growth?
Without compounding:
1000 + 1000 × 0.10 × t = 2000
100t = 1000
t = 10 years.
With compounding:
1000(1.1)t = 2000
The amount is still below double after 7 years and reaches/exceeds double during the 8th annual compounding period.
So it takes about 7.27 years mathematically, or 8 complete annual compounding periods to reach/exceed double.
Yes. Compounding gives exponential growth, while no-compounding growth is linear.
8. The population of a city is rising by about 3% every year. If the current population is 1.5 crore, what is the expected population after 3 years?
Population = 1.5 × (1.03)3 crore
≈ 1.6390905 crore
Approximately 1.64 crore.
9. In a laboratory, the number of bacteria in a certain experiment increases at the rate of 2.5% per hour. Find the number of bacteria at the end of 2 hours if the initial count is 5,06,000.
Number = 5,06,000 × (1.025)2
= 5,31,616.25
Approximately 5,31,616 bacteria.
Decline and Depreciation
When the value of an item decreases because of age or use, it is called depreciation.
After a decrease of r%:
New value = Original value × (1 − r)
Example
A TV costs ₹21,000 and depreciates by 5%.
New value = 21,000 × 0.95
= ₹19,950
Population decreasing by 10% for 3 decades
Population = 1250 × 0.9 × 0.9 × 0.9
= 911.25
Approximately 910 people.
Tricky Percentages – Would You Rather?
You have won a contest. The organisers offer you two options to choose from:
Option A: You deposit ₹100 and you get back ₹300.
Option B: You deposit ₹1000 and you get back ₹1500.
What is the percentage gain each option gives? You can choose any option only once. Which option would you choose? Why?
Option A:
Gain = ₹300 − ₹100 = ₹200
Gain percentage = 200/100 × 100 = 200%
Option B:
Gain = ₹1500 − ₹1000 = ₹500
Gain percentage = 500/1000 × 100 = 50%
So, Option A gives the larger percentage gain, while Option B gives a larger absolute gain in rupees.
A provision store is offering a stock clearance sale. Customers can choose one of the two options — 20% discount or ₹50 discount — for any purchase above ₹150. Which option would you choose if you want to:
A discount of 30% followed by another discount of 20% is not the same as a single 50% discount.
Example
Original cake price = ₹200
First discount = 30%
₹200 − ₹60 = ₹140
Second discount = 20% of ₹140 = ₹28
Final price = ₹140 − ₹28 = ₹112
A single 50% discount would make the price ₹100.
Successive discounts are calculated one after another.
A Mishap – Profit and Discount
Example 13: After Surbhi bought cookware from the wholesaler, she kept a profit margin of 50% on all the products. To clear off the remaining stock, she thought she would offer a 50% discount and come out without any loss.
(i) Do you think she didn’t make any loss?
(ii) If she had sold goods (originally) for ₹12,000 after discount, how much loss did she incur? What is the percentage loss?
(iii) What should have been the percentage discount offered so that she sold the goods at the price she had bought (i.e., no profit or loss)?
Let cost price = x.
After 50% profit:
Selling/marked price = 1.5x
After 50% discount:
= 1.5x × 0.5 = 0.75x
So the final selling price is only 75% of the cost price.
(i) She makes a 25% loss.
(ii)
0.75x = ₹12,000
x = ₹16,000
Loss = ₹16,000 − ₹12,000 = ₹4,000
Loss percentage = 4000/16000 × 100
= 25%
(iii)
She needs to reduce 1.5x to x.
Required discount = (1.5x − x)/1.5x × 100
= 33.33% approximately.
Ariba and Arun have some marbles. Ariba says, “The number of marbles with me is 120% of the marbles Arun has”. What would be an appropriate statement Arun could make comparing the number of marbles he has with Ariba’s?
Suppose Arun has 100 marbles.
Ariba has 120 marbles.
Arun’s marbles as a percentage of Ariba’s:
100/120 × 100 = 83.33%
Arun has about 83.33% as many marbles as Ariba.
Figure it Out – Final Questions
1. The population of Bengaluru in 2025 is about 250% of its population in 2000. If the population in 2000 was 50 lakhs, what is the population in 2025?
250% of 50 lakhs:
= 2.5 × 50
= 125 lakhs = 1.25 crore.
2. The population of the world in 2025 is about 8.2 billion. The populations of some countries in 2025 are given. Match them with their approximate percentage share of the worldwide population.
Germany – 83 million
India – 1.46 billion
Bangladesh – 175 million
USA – 347 million
Country
Approximate share
Germany
≈ 1%
India
≈ 18%
Bangladesh
≈ 2%
USA
≈ 4%
For example, India’s share:
1.46 ÷ 8.2 × 100 ≈ 17.8%
So India ≈ 18%.
3. The price of a mobile phone is ₹8,250. A GST of 18% is added to the price. Which of the following gives the final price of the phone including the GST?
4. The monthly percentage change in population (compared to the previous month) of mice in a lab is given: Month 1 change was +5%, Month 2 change was –2%, and Month 3 change was –3%. Which of the following statement(s) are true? The initial population is p.
(i) The population after three months was p × 0.05 × 0.02 × 0.03.
(ii) The population after three months was p × 1.05 × 0.98 × 0.97.
(iii) The population after three months was p + 0.05 – 0.02 – 0.03.
(iv) The population after three months was p.
(v) The population after three months was more than p.
(vi) The population after three months was less than p.
After +5%: multiply by 1.05.
After −2%: multiply by 0.98.
After −3%: multiply by 0.97.
Population = p × 1.05 × 0.98 × 0.97
The product is less than 1, so the final population is less than p.
Correct statements: (ii) and (vi).
5. A shopkeeper initially set the price of a product with a 35% profit margin. Due to poor sales, he decided to offer a 30% discount on the selling price. Will he make a profit or a loss? Give reasons for your answer.
Let cost price = ₹100.
35% profit means marked/selling price before discount = ₹135.
30% discount on ₹135 = ₹40.50.
Final selling price = ₹135 − ₹40.50 = ₹94.50.
Cost price = ₹100.
Loss = ₹5.50, so there is a 5.5% loss.
6. What percentage of area is occupied by the region marked ‘E’ in the figure?
From the textbook dot-grid figure, the complete outer rectangle can be considered as 4 × 4 = 16 equal square units.
Region E is a triangle formed from a 2 × 2 square.
Area of the 2 × 2 square = 4 square units.
The diagonal divides it into two equal triangles.
Area of E = 4 ÷ 2 = 2 square units.
Percentage = 2/16 × 100
= 12.5%
7. What is 5% of 40? What is 40% of 5? What is 25% of 12? What is 12% of 25? What is 15% of 60? What is 60% of 15? What do you notice? Can you make a general statement and justify it using algebra, comparing x% of y and y% of x?
5% of 40 = 2
40% of 5 = 2
25% of 12 = 3
12% of 25 = 3
15% of 60 = 9
60% of 15 = 9
The values are equal.
x% of y = x/100 × y
y% of x = y/100 × x
Both = xy/100
Therefore, x% of y = y% of x.
8. A school is organising an excursion for its students. 40% of them are Grade 8 students and the rest are Grade 9 students. Among these Grade 8 students, 60% are girls.
(i) What percentage of the students going to the excursion are Grade 8 girls?
(ii) If the total number of students going to the excursion is 160, how many of them are Grade 8 girls?
Grade 8 students = 40%.
60% of these Grade 8 students are girls.
Grade 8 girls = 60% of 40%
= 0.60 × 40%
= 24%
For 160 students:
24% of 160 = 0.24 × 160
= 38.4
Since the textbook gives a percentage estimate, this corresponds to approximately 38 students. In an actual school count, the given percentages and total would need to be compatible with whole students.
9. A shopkeeper sells pencils at a price such that the selling price of 3 pencils is equal to the cost of 5 pencils. Does he make a profit or a loss? What is his profit or loss percentage?
Let cost of 1 pencil = ₹1.
Cost of 5 pencils = ₹5.
Selling price of 3 pencils = ₹5.
Therefore, selling price of 1 pencil = ₹5/3.
Profit per pencil = 5/3 − 1 = 2/3.
Profit percentage = (2/3) ÷ 1 × 100
= 66.67% approximately.
So, the shopkeeper makes a profit.
10. The bus fares were increased by 3% last year and by 4% this year. What is the overall percentage price increase in the last 2 years?
Take original fare = 100.
After 3% increase = 103.
After another 4% increase:
103 × 1.04 = 107.12
Overall increase = 7.12%.
11. If the length of a rectangle is increased by 10% and the area is unchanged, by what percentage (exactly) does the breadth decrease by?
Original length = L.
Original breadth = B.
New length = 1.10L.
Area remains the same:
1.10L × new breadth = L × B
New breadth = B/1.10 = 10B/11.
Decrease = B − 10B/11 = B/11.
Percentage decrease = 1/11 × 100
= 100/11% = 9.09% approximately.
12. The percentage of ingredients in a 65 g chips packet is shown in the picture. Find out the weight each ingredient makes up in this packet.
13. Three shops sell the same items at the same price. The shops offer deals as follows:
Shop A: “Buy 1 and get 1 free”
Shop B: “Buy 2 and get 1 free”
Shop C: “Buy 3 and get 1 free”
(i) If the price of one item is ₹100, what is the effective price per item in each shop? Arrange the shops from cheapest to costliest.
(ii) For each shop, calculate the percentage discount on the items.
(iii) Suppose you need 4 items. Which shop would you choose? Why?
Shop A: Buy 1, get 1 free.
Pay ₹100 for 2 items.
Effective price = ₹50 per item.
Discount = 50%.
Shop B: Buy 2, get 1 free.
Pay ₹200 for 3 items.
Effective price = ₹66.67 per item.
Discount = 33.33%.
Shop C: Buy 3, get 1 free.
Pay ₹300 for 4 items.
Effective price = ₹75 per item.
Discount = 25%.
Shop
Effective price/item
Discount
A
₹50
50%
B
₹66.67
33.33%
C
₹75
25%
For exactly 4 items, Shop A can be used by buying 2 items and getting 2 free, subject to the offer’s interpretation. The textbook asks students to consider the deal structure and explain their reasoning.
14. In a room of 100 people, 99% are left-handed. How many left-handed people have to leave the room to bring that percentage down to 98%?
Initially:
Left-handed = 99
Right-handed = 1
Suppose x left-handed people leave.
Left-handed remaining = 99 − x
Total remaining = 100 − x
We need:
(99 − x)/(100 − x) = 98/100
100(99 − x) = 98(100 − x)
9900 − 100x = 9800 − 98x
100 = 2x
x = 50
Therefore, 50 left-handed people must leave.
15. Look at the following graph. Based on the graph, which of the following statement(s) are valid?
(i) People in their twenties are the most computer-literate among all age groups.
(ii) Women lag behind in the ability to use computers across age groups.
(iii) There are more people in their twenties than teenagers.
(iv) More than a quarter of people in their thirties can use computers.
(v) Less than 1 in 10 aged 60 and above can use computers.
(vi) Half of the people in their twenties can use computers.
(i) valid
(ii) valid.
(iii) not valid.
(iv) not valid.
(v) valid
(vi) not valid
Valid statements: (i), (ii), and (v).
Quick Revision Sheet
Topic
Rule
Percentage
x% = x/100
Fraction to percentage
Fraction × 100
Percentage of quantity
Percentage/100 × quantity
Percentage increase
Increase/original × 100
Percentage decrease
Decrease/original × 100
Profit
SP − CP
Loss
CP − SP
Profit %
Profit/CP × 100
Loss %
Loss/CP × 100
Discount
Discount/Marked Price × 100
After r% increase
Original × (1 + r)
After r% decrease
Original × (1 − r)
No compounding
A = P(1 + rt)
Compounding
A = P(1 + r)t
Remember: Whenever you see a percentage increase or decrease, the percentage is applied to the value that exists at that stage. This is especially important in successive discounts and compound growth.
Important Answers at a Glance
Question
Answer
3/5 as percentage
60%
15 out of 25
60%
15 out of 80
18.75%
25% of 160
40
16% of 250
40
62% of 360
223.2
140% of 40
56
3/4 of 60 ml
45 ml
Full coffee plantation
90 days
90-minute badminton session
9 min, 72 min, 9 min
₹8250 + 18% GST
₹9735
₹20,000 at 10% for 2 years compounded
₹24,200
₹50,000 at 7% for 3 years, no compounding
₹10,500 interest
TV ₹21,000 depreciated 5%
₹19,950
Region E
12.5%
10% + 4% successive increase
7.12% overall for 3% then 4%
Prepare with this NCERT Ganita Prakash worksheet for Chapter 1. It includes important questions and revision exercises to help students practise key concepts, strengthen their understanding, and prepare effectively for class tests and exams.
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