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Solutions

Overview

Step-by-step NCERT solutions for Fractions in Disguise (Chapter 8, NCERT Class 8 Mathematics) — every question and answer worked out in full, not just the final result. You can also read the Fractions in Disguise textbook chapter.

Solved

What these solutions cover

All 53 questions in Fractions in Disguise are solved in the PDF. Here's what's inside, exercise by exercise:

Fractions as Percentages

  1. Express the following fractions as percentages.
    • (i) 3/5
    • (ii) 7/14
    • (iii) 9/20
    • (iv) 72/150
    • (v) 1/3
    • (vi) 5/11
  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
  3. In a school, 15 of the 80 students come to school by walking. What percentage of the students come by walking?
  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%, 84%, 72%, 93%
  5. Pairs of quantities are shown below. Identify and write appropriate symbols '>', '<', '=' in the blanks. Try to do it without calculations.
    • (i) 50% ____ 5%
    • (ii) 5/10 ____ 50%
    • (iii) 3/11 ____ 61%
    • (iv) 30% ____ 1/3

Percentage of Some Quantity

  1. Find the missing numbers. The first problem has been worked out.
    • (i) Bar: 100% = 60, 20% = ? (worked); second bar: total = 75, 20% = ?
    • (ii) Bar: 20% = 12, total = ? (missing); second bar: total = 90, 20% = ?
    • (iii) Bar: total = 140, 25% = ? (missing); second bar: 25% = 140, total = ?
  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?
  4. Pairs of quantities are shown below. Identify and write appropriate symbols '>', '<', '=' in the boxes. Visualising or estimating can help.
    • (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
  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.
  6. Fill in the blanks:
    • (i) 3 is ____ % of 300.
    • (ii) _____ is 40% of 4.
    • (iii) 40 is 80% of _____.
  7. Is 10% of a day longer than 1% of a week? Create such questions and challenge your peers.
  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 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. What do you observe?
  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?
  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?
  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.
  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?

Using Percentages

  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?
  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?
  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?
  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?
  5. The petrol price in 2015 was ₹60 and ₹100 in 2025. What is the percentage increase in the price of petrol?
    • (i) 50%
    • (ii) 40%
    • (iii) 60%
    • (iv) 66.66%
    • (v) 140%
    • (vi) 160.66%
  6. 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?
  7. 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?
  8. 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.)
  9. A number increased by 20% becomes 90. What is the number?
  10. 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.
  11. 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
  12. 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…

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.
  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.
  3. Do you observe anything interesting in the solutions of the two questions above? Share and discuss.

Growth and Compounding — Formulas and Applications

  1. 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)
  2. 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?
  3. 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?
  4. 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?
  5. 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?
  6. 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.

Percentage Applications

  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?
  2. The population of the world in 2025 is about 8.2 billion. Match each country's 2025 population with its approximate percentage share of the worldwide population: Germany 83 million, India 1.46 billion, Bangladesh 175 million, USA 347 million. (Percentage tiles to choose from: 13%, 8%, 18%, 10%, 1%, 35%, 2%, 2%, 0.1%.) [Hint: Writing these numbers in the standard form and estimating can help.]
  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 including GST?
    • (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
  4. The monthly percentage change in population of mice in a lab (compared to the previous month) is: Month 1 +5%, Month 2 −2%, Month 3 −3%. The initial population is p. Which statement(s) are true?
    • (i) Population after three months = p × 0.05 × 0.02 × 0.03.
    • (ii) = p × 1.05 × 0.98 × 0.97.
    • (iii) = p + 0.05 − 0.02 − 0.03.
    • (iv) = p.
    • (v) more than p.
    • (vi) less than p.
  5. A shopkeeper initially 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? Give reasons.
  6. What percentage of area is occupied by the region marked 'E' in the figure? (The figure is a 6 × 6 square dot grid divided into regions A, B, C, D and E.)
  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?
  8. A school is organising an excursion. 40% of the students are Grade 8 and the rest are Grade 9. Among the Grade 8 students, 60% are girls.
    • (i) What percentage of all the students are Grade 8 girls?
    • (ii) If the total number going is 160, how many are Grade 8 girls?
  9. A shopkeeper sells pencils such that the selling price of 3 pencils equals the cost of 5 pencils. Does he make a profit or a loss? What is his profit or loss percentage?
  10. The bus fares were increased by 3% last year and by 4% this year. What is the overall percentage price increase over the last 2 years?
  11. If the length of a rectangle is increased by 10% and the area is unchanged, by what percentage (exactly) does the breadth decrease?
  12. The percentage of ingredients in a 65 g chips packet is: Potato 70%, Vegetable oil 24%, Salt 3%, Spices 3%. Find the weight of each ingredient in the packet.
  13. Three shops sell the same items at the same price. Shop A: 'Buy 1 get 1 free', Shop B: 'Buy 2 get 1 free', Shop C: 'Buy 3 get 1 free'.
    • (i) If one item costs ₹100, what is the effective price per item in each shop? Arrange cheapest to costliest.
    • (ii) Calculate the percentage discount in each shop.
    • (iii) If you need 4 items, which shop would you choose? Why?
  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%?
  15. The graph 'Ability to use computers by age and gender (2023)' shows Female/Male percentages: Children 4%/5%, Teenage 24%/29%, Twenties 26%/37%, Thirties 14%/25%, Forties 7%/14%, Fifties 4%/9%, Seniors 2%/4%. Which statement(s) 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…
Sample

Worked examples

3 questions from Fractions in Disguise, solved step by step.

Fractions as Percentages

Express the following fractions as percentages. (i) 3/5 (ii) 7/14 (iii) 9/20 (iv) 72/150 (v) 1/3 (vi) 5/11

To express a fraction as a percentage, multiply by 100.

(i) 3/5 × 100 = 60%

(ii) 7/14 = 1/2; 1/2 × 100 = 50%

(iii) 9/20 × 100 = 900/20 = 45%

(iv) 72/150 × 100 = 7200/150 = 48%

(v) 1/3 × 100 = 100/3 = 33.33...% ≈ 33⅓%

(vi) 5/11 × 100 = 500/11 = 45.45...% ≈ 45 5/11%

Answer: (i) 60% (ii) 50% (iii) 45% (iv) 48% (v) 33⅓% (vi) 45 5/11%

Percentage of Some Quantity

Find the missing numbers. The first problem has been worked out. (i) Bar: 100% = 60, 20% = ? (worked); second bar: total = 75, 20% = ? (ii) Bar: 20% = 12, total = ? (missing); second bar: total = 90, 20% = ? (iii) Bar: total = 140, 25% = ? (missing); second bar: 25% = 140, total = ?

(i) Worked example: 20% of 60 = (20/100) × 60 = 12.

For the second bar: 20% of 75 = (20/100) × 75 = 15.

(ii) If 20% of total = 12, then total = 12 / 0.20 = 60.

For the second bar: 20% of 90 = (20/100) × 90 = 18.

(iii) 25% of 140 = (25/100) × 140 = 35.

For the second bar: if 25% = 140, then total = 140 / 0.25 = 560.

Answer: (i) 12 (worked), 15; (ii) total = 60, value = 18; (iii) value = 35, total = 560

Using Percentages

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?

CP = ₹475. Profit margin (on cost) = 50%.

Profit = 50% of 475 = 0.50 × 475 = ₹237.50.

SP = CP + Profit = 475 + 237.50 = ₹712.50.

Answer: The selling price should be ₹712.50.

All 53 questions in Fractions in Disguise are solved step by step in the Solutions PDF above.

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