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08
NCERT Solutions · Maths Ch 8
Fractions in Disguise
53 questions · 5 exercises
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Ex 8.1
Ex 8.2
Ex 8.3
Ex 8.4
Ex 8.5
NCERT answers with full exam-style working, step by step. Tap a question to open its solution.
1
EXERCISE 8.1 · 5 QUESTIONS
Percentages
Q1
Express the following fractions as percentages. (i) 3/5 (ii) 7/14 (iii) 9/20 (iv) 72/150 (v) 1/3 (vi) 5/11
(3 marks)
Q2
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
(2 marks)
Q3
In a school, 15 of the 80 students come to school by walking. What percentage of the students come by walking?
(2 marks)
Q4
A group of friends is participating in a long-distance run. The positions of each of them after 15 minutes are shown in the picture. Match (among the given options) what percentage of the race each of them has approximately completed. Options: 55%, 20%, 38%, 72%, 84%, 93%.
Figure: a track from Start to Finish; A is about one-third of the way, B just past halfway, C about three-quarters of the way, D very close to the finish.
(2 marks)
Q5
Write >, (3 marks)
2
EXERCISE 8.2 · 12 QUESTIONS
Using percentages
Q1
Find the missing numbers in the bar models. (i) [worked] One part of a bar of 5 equal parts is 20%; a bar of 5 parts shows 75 as 100%, and 4 parts are 60. (ii) A bar of 10 equal parts is 100%; what % is one part? A bar of 10 parts shows 90 as 100%; what is the value of 6 parts? (iii) A bar of 4 equal parts is 100%; what % is one part? A bar of 4 parts shows 140 as 100%; what is the value of 3 parts?
(3 marks)
Q2
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 marks)
Q3
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?
(2 marks)
Q4
Write >, (3 marks)
Q5
Fill in the blanks. (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 ___.
(3 marks)
Q6
Fill in the blanks: (i) 3 is ___% of 300. (ii) ___ is 40% of 4. (iii) 40 is 80% of ___.
(2 marks)
Q7
Is 10% of a day longer than 1% of a week? Create such questions and challenge your peers.
(3 marks)
Q8
Mariam's bull: on day 1 it is given 2 units of fodder and eats 1; day 2 given 3, eats 2; day 3 given 4, eats 3; … on day 99 given 100, eats 99. Represent these quantities as percentages. What do you observe?
(3 marks)
Q9
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 for the entire plantation, assuming the rate of work stays the same? Why is this assumption necessary?
(2 marks)
Q10
The badminton coach plans warm up : play : cool down as 10% : 80% : 10%. If the training lasts 90 minutes, how long should each activity be done?
(3 marks)
Q11
About 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.
(2 marks)
Q12
A halwa recipe for 4 people has Rava 40%, Sugar 40%, Ghee 20%. (i) For 8 people, what is the proportion of each ingredient? (ii) If the total weight of the ingredients is 2 kg, how much rava, sugar and ghee are present?
(3 marks)
3
EXERCISE 8.3 · 12 QUESTIONS
Profit, loss and change
Q1
A shopkeeper buys a geometry box for ₹75 and sells it for ₹110. What is his profit margin with respect to the cost?
(2 marks)
Q2
The cost of materials for a chair is ₹475 and the carpenter wants a profit margin of 50%. At what price should he sell a chair?
(3 marks)
Q3
The total sales of a company (revenue) was ₹2.5 crore last year. They had a profit margin of 25%. What was the total expenditure (costs) of the company last year?
(2 marks)
Q4
A clothing shop offers a 25% discount on all shirts. If the original price of a shirt is ₹300, how much will Anwar pay?
(2 marks)
Q5
The petrol price was ₹60 in 2015 and ₹100 in 2025. What is the percentage increase? (i) 50% (ii) 40% (iii) 60% (iv) 66.66% (v) 140% (vi) 160.66%
(2 marks)
Q6
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?
(2 marks)
Q7
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?
(3 marks)
Q8
The price of 1 kg of rice was ₹38 in 2024 and ₹42 in 2025. What is the rate of inflation?
(2 marks)
Q9
A number increased by 20% becomes 90. What is the number?
(2 marks)
Q10
A milkman sold two buffaloes for ₹80,000 each. On one he made a profit of 5% and on the other a loss of 10%. Find his overall profit or loss.
(3 marks)
Q11
The elephant population increased by 5% in the last decade. If the population last decade was 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
(2 marks)
Q12
Which 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.
(2 marks)
4
EXERCISE 8.4 · 9 QUESTIONS
Compounding
Q1
Bank of Yahapur offers 10% p.a. Compare how much one gets on a deposit of ₹20,000 for 2 years with and without compounding annually.
(3 marks)
Q2
Bank of Wahapur offers 5% p.a. Compare how much one gets on a deposit of ₹20,000 for 4 years with and without compounding annually.
(3 marks)
Q3
Do you observe anything interesting in the solutions of the two questions above?
(1 mark)
Q4
Jasmine invests amount p for 4 years at 6% p.a. Which expression(s) describe the total amount 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)
(2 marks)
Q5
The post office offers 7% p.a. How much interest would one get on ₹50,000 for 3 years without compounding? How much more would one get if it was compounded?
(3 marks)
Q6
Giridhar borrows ₹12,500 at 12% p.a. for 3 years without compounding, and Raghava borrows the same amount for the same time at 10% p.a. compounded annually. Who pays more interest and by how much?
(3 marks)
Q7
₹1000 grows at 10% p.a. How long will it take to double with and without compounding? Is compounding an example of exponential growth and not-compounding an example of linear growth?
(2 marks)
Q8
The population of a city rises by about 3% every year. If the current population is 1.5 crore, what is the expected population after 3 years?
(2 marks)
Q9
Bacteria increase at 2.5% per hour. Find the number at the end of 2 hours if the initial count is 5,06,000.
(2 marks)
5
EXERCISE 8.5 · 15 QUESTIONS
End of chapter
Q1
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?
(2 marks)
Q2
The world population in 2025 is about 8.2 billion. Match Germany (83 million), India (1.46 billion), Bangladesh (175 million) and USA (347 million) with their approximate percentage share. Options: 13%, 8%, 18%, 10%, 1%, 35%, 2%, 2%, 0.1%.
(2 marks)
Q3
The price of a mobile phone is ₹8,250. A GST of 18% is added. Which gives the final price? (i) 8250 + 18 (ii) 8250 + 1800 (iii) 8250 + 18/100 (iv) 8250 × 18 (v) 8250 × 1.18 (vi) 8250 + 8250 × 0.18 (vii) 1.8 × 8250
(2 marks)
Q4
Mice population changes: month 1 +5%, month 2 −2%, month 3 −3%. Initial population p. Which are true? (i) p × 0.05 × 0.02 × 0.03 (ii) p × 1.05 × 0.98 × 0.97 (iii) p + 0.05 − 0.02 − 0.03 (iv) The population was p. (v) It was more than p. (vi) It was less than p.
(2 marks)
Q5
A shopkeeper set the price of a product with a 35% profit margin. Due to poor sales, he offered a 30% discount on the selling price. Will he make a profit or a loss?
(3 marks)
Q6
What percentage of area is occupied by the region marked E in the figure?
Figure (on dot paper): an 8 × 8 square. The left half is split into a 4 × 4 square A (top) and a 4 × 4 square (bottom) cut by a diagonal into triangles D (upper-left) and E (lower-right); the right half holds B (4 × 6) and C (4 × 2).
(2 marks)
Q7
What is 5% of 40? 40% of 5? 25% of 12? 12% of 25? 15% of 60? 60% of 15? What do you notice? Make a general statement comparing x% of y and y% of x and justify it using algebra.
(3 marks)
Q8
40% of the students going on an excursion are in Grade 8; the rest are in Grade 9. Among the Grade 8 students, 60% are girls. (i) What percentage of all the students are Grade 8 girls? (ii) If 160 students are going, how many are Grade 8 girls?
(3 marks)
Q9
A shopkeeper sells pencils at a price such that the selling price of 3 pencils equals the cost of 5 pencils. Does he make a profit or a loss? What is the percentage?
(3 marks)
Q10
Bus fares were increased by 3% last year and by 4% this year. What is the overall percentage increase in the last 2 years?
(2 marks)
Q11
If the length of a rectangle is increased by 10% and the area is unchanged, by what percentage (exactly) does the breadth decrease?
(3 marks)
Q12
The chips packet (net quantity 65 g) shows: Potato 70%, Vegetable oil 24%, Salt 3%, Spices 3%. Find the weight of each ingredient.
(3 marks)
Q13
Three shops: A “Buy 1 get 1 free”, B “Buy 2 get 1 free”, C “Buy 3 get 1 free”. (i) If one item costs ₹100, what is the effective price per item in each shop? Arrange from cheapest to costliest. (ii) Calculate the percentage discount for each shop. (iii) If you need 4 items, which shop would you choose? Why?
(3 marks)
Q14
In a room of 100 people, 99% are left-handed. How many left-handed people have to leave to bring that percentage down to 98%?
(2 marks)
Q15
Graph: ability to use a computer by age and gender (2023). Female / Male: Children 4% / ~5%, Teenage 24% / 29%, Twenties 26% / 37%, Thirties 14% / 25%, Forties 7% / 14%, Fifties 4% / 9%, Seniors 2% / 4%. Which statements are valid? (i) People in their twenties are the most computer-literate. (ii) Women lag behind 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+ can use computers. (vi) Half of the people in their twenties can use computers.
(2 marks)