Each of our Ganita Prakash Class 8 Worksheet and NCERT Class 8 Maths Chapter 1 Fractions in Disguise Worksheet with Answers focuses on conceptual clarity.
Fractions in Disguise Worksheet Class 8
Class 8 Maths Fractions in Disguise Worksheet
Fractions in Disguise Class 8 Ganita Prakash Worksheet
Rajat, Mona and Vasant are the students of class VIII. Today, the Maths teacher is distributing the answer sheets of Maths exam to the students.
Rajat: I got 68 marks out of 100.
Maya: I got 72 marks out of 100.
Vasant: Hurray! I got 92 percent marks in the Maths exam.
Rajat: 92 percent! What kind of number is it?
Maths Teacher: It means he got 92 marks out of 100. And, the word per cent means per _____. It is represented by the symbol ” ____” So, we can say that percentages are simply fractions where the denominator is _____.
Question 1.
Answer the following questions.
(a) What does 72% marks mean out of 100 marks?
(b) What is the meaning of 50% of 100 marks?
(c) What does 68 marks out of 100 mean in per cent?
Answer:
(a) 72
(b) 50
(c) 68%
Question 2.
Fill in the boxes.
Answer:
(a) 42
(b) 67
(c) 100
(d) 97, 100
Expressing Fractions as Percentages
Sara, Maya’s elder sister, is reviewing her performance in a practice test for her sports academy. The minimum requirement for selection is 70%. Sara answered 3 out of 4 questions correctly. Maya is curious about how to express her result as a percentage.
Maya: How did you do this?
Sara: We can convert a fractional number into percentage by multiplying by 100, and adding the symbol %, and simplifying it, if needed.
Question 3.
Express the following fractions as percentages.
(a) \(\frac{35}{100}\)
(b) \(\frac{9}{100}\)
(c) \(\frac{3}{25}\)
(d) \(\frac{11}{20}\)
(e) \(\frac{7}{8}\)
(f) \(\frac{4}{5}\)
Answer:
(a) 35%
(b) 18%
(c) 12%
(d) 55%
(e) 87.5%
(f) 80%
Question 4.
Anjali has 32 stickers, out of which 8 are star-shaped. What percentage of her stickers are star shaped?
Answer:
25%
Question 5.
Complete the given model.
Maga: Suppose, if I got 85% marks. Can we express it infraction?
Sara: Yes, a percentage can also be expressed by any of the fractions that are equivalent to \(\frac{a}{100}\) , where a is the value of the given percentage. So, 85% can be expressed in a fraction as 85% = \(\frac{85}{100}\) = \(\frac{17}{20}\)
Answer:
Question 6.
Express the following percentages into fractions, simplify them if required,
(a) 20%
(b) 60%
(c) 2%
Answer:
(a) \(\frac{1}{5}\)
(b) \(\frac{3}{5}\)
(c) \(\frac{1}{50}\)
Question 7.
Compare the following pairs and fill in the correct symbol (>, <, =).
Do it mentally, without doing detailed calculations.
(a) 75% ________ 25%
(b) \(\frac{4}{10}\) ________ 35%
(c) \(\frac{7}{10}\) ________ 40%
(d) 60% _______ \(\frac{3}{5}\)
Answer:
(a) >
(b) >
(c) <
(d) =
Percentage of Some Quantity
Question 8.
Riya and Rohit eat biscuits of different varieties. Riya’s biscuits contain 30% sugar, while Rohit’s biscuits contain 20% sugar. If Riya eats 150 g of biscuits and Rohit eats 180 g of biscuits, who consumes more sugar?
Answer:
Riya
Question 9.
A bakery produces bread, and 5% of the weight of each loaf is sugar. If a loaf weighs 1.2 kg, how much sugar is in each loaf?
Answer:
60g
Question 10.
A recipe for vegetable pulao for 5 people In a hostel kitchen uses the ingredients in the following proportions:
Rice – 50%, Vegetables – 30%, Spices, Oil, and Condiments – 20%.
(a) If the pulao is to be prepared for 10 people, what will be the proportion of each ingredient?
(b) If the total weight of ingredients used is 3 kg, find the weight of rice and vegetables.
Answer:
(a) Rice – 5096, Vegetables – 30%, Spices, Oil, and Condiments – 20%
(b) Rice – 1 kg 500 g, Vegetables – 900 g
Question 11.
A basketball coach in Bengaluru plans a practice session so that the time spent on warm-up, practice and relaxation is in the ratio 15% : 70% : 15%. If the total duration of the session is 120 minutes, how long should each activity last?
Answer:
Warmup – 18 minutes,
Practice – 84 minutes,
Relaxation – 18 minutes.
Question 12.
A farmer in Punjab harvested 480 kg of rice last year. This year, he harvested 720 kg of rice from the same field. What percentage of last year’s harvest is this year’s harvest?
Answer:
150%
Question 13.
Find the value of the following, and also draw their bar models.
(a) 30% of 200
(b) 18% of 150
Answer:
(a) 60
(B) 27
Question 14.
Fill in the blanks appropriately:
If 40% of p is 120, 20% of p is _______, 80% of p is _______, 150% of p is _______.
Answer:
60, 240, 450.
Question 15.
Find 70% of 20 and 20% of 70;
35% of 40 and 40% of 35;
25% of 80 and 80% of 25.
Make a general statement comparing x% of y and y% of x, and justify it using algebra.
Answer:
14, 14; 20,20
Using Percentages
To Compare Proportions
Question 16.
Mehul scored 36 marks out of 45 in Mathematics and 68 marks out of 80 in Science. His friend Aarav says Mehul did better in Science because he scored more marks. Do you agree? Justify your answer using percentages.
Answer:
Yes
Know Your Contents (KYC)
Food labels tell us how much of each ingredient is present in a product. Percentages make it easier to compare products and decide which one is healthier.
Question 17.
Riga and Kabir are comparing two brands of instant fruit juice mix—Fresh Sip and Juicy Drop.
Fresh Sip (Total weight = 200 g):
Sugar – 90 g;
Fruit pulp – 80 g
Food additives – 30 g
Juicy Drop (Total weight = 250 g):
Sugar – 100 g;
Fruit pulp – 120 g
Food additives – 30 g
(a) Find the percentage of each ingredient in both brands.
Answer:
Fresh Sip: Sugar = 45%, Fruit pulp powder = 40%, Food additives = 15%
Juicy Drop: Sugar 40%, Fruit pulp powder = 48%, FQod additives = 12%
(b) Check whether the percentages in each product add up to 100%.
Answer:
Yes
Percentage Increase and Decrease
Question 18.
The price of a school bag in 2021 was ₹800. Ia 2024, its price increased to ₹ 1,000. Find the percentage increase in the price.
Answer:
25%
Question 19.
Before renovation, the average number of visitors to a public library in Kolkata was 300 per day. After renovation, it dropped to 210 per day. Find the percentage decrease.
Answer:
30%
Profit and Loss
In daily life, shopkeepers calculate profit or loss by comparing the Cost Price (CP) and Selling Price (SP) of goods. Percentages help them understand how much they gain or lose.
Question 20.
Neeraj buys a bicycle from a wholesaler for ₹4,000 and marks its price as ₹5,200. After bargaining, he sells it for ₹4,800.
(a) Find the profit made by Neeraj.
(b) Claculate the percentage profit
Answer:
(a) ₹ 800
(b) 20%
Question 21.
Aruta bought 20 kg of apples at 6O per kg. Due to spoilage, she sold aLL of them for 1,O2O.
(a) Find the total cost price.
(b) Find the loss incurred.
(c) Calculate the loss percent.
Answer:
(a) ₹ 1200
(b) ₹ 180
(c) 15%
Question 22.
Ravi bought two bicycLes for ₹ 8,OOO each. He sold one at a profit of 10% and the other at a loss of 5%. Find his overall profit or loss.
Answer:
profit of ₹ 400
Question 23.
A clothinq store in Indore offers a 25% discount on a jacket marked at ₹2,400.
(a) Find the selling price of the jacket.
(b) If the cost of the jacket is 1600 find the percentage profit
Answer:
(a) ₹ 1800
(b) 12.5%
Taxes
Taxes like GST are a part of the price we pay and this amount goes to the government.
Question 24.
XY Electronics sells LED bulbs at ₹180 each. GST is 18%. A customer buys 5 bulbs,
(a) Calculate the total GST paid.
(b) Find the total amount the customer must pay.
Answer:
(a) ₹ 162
(b) ₹ 1062
Growth arid Compounding
Banks pay interest on deposits. Fixed deposits (FDs) are investments where money is deposited for a fixed period at a fixed interest rate.
Question 25.
Bank of Himtara offers an interest rate of 8% perannum. Compare how much one gets if they deposit ₹15,000 for a period of 3 years, with compounding and without compounding annually.
Answer:
Total interest: With compounding – ₹ 3895.5O
Without compounding – ₹ 36OO
Question 26.
Anil borrows ₹ 18,000 at 10% perannum for 3 years without compounding, while Sunil borrows the same amount at 8% perannum, compounded annually. Who pays more interest, and by how much?
Answer:
Anil pays ₹ 725.40 more.
Question 27.
The population of a town increases by 4% every year. If the current population is 2,00,000, what will be the expected population after 5 years?
Answer:
243331
Decline
Depreciation is the reduction in the value of an asset over time due to wear, use, or aging. It means things like vehicles, machines, or equipment become less valuable as they get older or are used.
Question 28.
A car showroom sells a car for ₹ 6,50,000. Due to usage, the car depreciates by 12% each year. Find the expected value of the car after 3 years.
Answer:
₹ 44 2956.80
Tricky Percentages
Question 29.
You won a small contest at school. The organizers offer two options:
Option A: Deposit ₹200 and get back ₹500.
Option B: Deposit ₹800 and get back ₹1,200.
Which option gives a better percentage gain?
Answer:
Option A
Question 30.
Two bcikenes SweetTreat and SugarRush, offer dlscounts oft cakes:
SweetTreat: 20% + 15% discount SgarRush: 35% discount
If a cake costs 40O, whtch bakery gives the cheaper price?
Answer:
Sugar Rush
Question 31.
A provision store is offering two options for a clearance sale on items above ₹300:
• Option A: 30% discount
• Option B: ₹ 120 off
Which option should a customer choose, if they want to buy:
(a) Items worth ₹ 350?
(b) Items worth ₹ 450?
(c) Items worth ₹ 600?
Answer:
(a) Option B
(b) Option A
(c) Option A.
Question 32.
After buying toys at wholesale prices, Rahul marked them up by 60%. Later, he gave a 30% discount during a festival sale. Did Rahul make a profit or loss? Find the percentage profit or loss.
Answer:
Percentage profit = 12%
Question 33.
After buying sports goods from a distributor, Neka marked all items at a 40% profit. Later, to clear old stock, she announced a 40% discount, thinking she would neithr gain nor lose money.
(a) Do you think Neha avoided a loss? Explain.
(b) What discount should Neha have offered to sell the goods at the cost price?
Answer:
(a) Loss of 16%
(b) Discount ≈ 29%
Question 34.
A shopkeeper sells erasers at a price suck that the selling price of 4 erasers is equal to the cost price of 6 erasers. Does the shopkeeper make a profit or a loss? Find his profit or loss percentage.
Answer:
Profit, Profit % = 50%
Question 35.
Three stores sell the same brand of water bottles at the same marked price. The stores offer the following schemes:
Store X: Buy 1, Get 1 Free!
Store Y: Buy 3, Get 1 Free!
Store Z: Buy 4, Get 2 Free!
If the price of one bottle is ₹150, find the effective price per bottle in each store. Arrange the stores from cheapest to costliest.
Answer:
Store X: ₹ 75,
Store Y: ₹ 112.5O,
Store Z: 100
Store X < Store Z < Store Y
Worksheet On Fractions in Disguise Class 8
A. Choose the correct option.
1. Which of the following represents 45% as a fraction in simplest form?
(a) \(\frac{45}{10}\)
(b) \(\frac{9}{20}\)
(c) \(\frac{45}{100}\)
(d) \(\frac{5}{9}\)
Answer:
(b) \(\frac{9}{20}\)
2. What does 80% of 250 equal?
(a) 180
(b) 200
(c) 225
(d) 250
Answer:
(b) 200
3. A number is increased by 10% and then decreased by 10%. The final result is:
(a) Same as original
(b) Greater than original
(c) Less than original
(d) Double the original
Answer:
(c) Less than original
4. If the cost price of an item is ₹400 and it is sold at a loss of 10%, the selling price is:
(a) ₹ 360
(b) ₹ 380
(c) ₹ 390
(d) ₹ 410
Answer:
(a) ₹ 360
5. Which of the following is greater?
(a) \(\frac{3}{5}\)
(b) 55%
(c) 0.5
(d) All are equal
Answer:
(a) \(\frac{3}{5}\)
6. A shopkeeper marks goods 50% above the cost price and gives a discount of 20%. He makes:
(a) Profit
(b) Loss
(c) No profit, no loss
(d) Cannot be determined
Answer:
(a) Profit
Directions. (For Q.7 – 8): In the following questions, a statement of Assertion (A) is followed by a statement of Reason (R). Choose the correct option as:
(a) Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).
(b) Both Assertion (A) and Reason (R) are true but Reason (R) is not the correct explanation of Assertion (A).
(c) Assertion (A) is true but Reason (R) is false.
(d) Assertion (A) is false but Reason (R) is true.
7. Assertion (A): If the price of a book increases by 20% and then decreases by 20%, the final price is less than the original price.
Reason (R): Percentage increase and decrease are always calculated on the same base value.
Answer:
(c) Assertion (A) is true but Reason (R) is false.
8. Assertion (A): 40% of 60 is equal to 60% of 40.
Reason (R): x % of y = y% of x.
Answer:
(a) Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).
B. Fill in the blanks.
1. Percent means out of ______.
Answer:
hundred
2. 65% can be written as the fraction ______.
Answer:
\(\frac{13}{20}\)
3. If 10% of a number is 40, then the number is ______.
Answer:
400
4. A discount of 25% means the customer pays ______% of the marked price
Answer:
75
C. State whether the following statements are true (T) or false (F).
1. 100% of a quantity is equal to the quantity itself.
Answer:
True
2. If the area of a rectangle remains constant, increasing the length will increase the breadth.
Answer:
false
3. A percentage can be greater than 100.
Answer:
True
4. Successive discounts of 20% and 10% are equal to a single discount of 30%.
Answer:
false
D. Solve the following.
Question 1.
Aarav scored 54 marks out of 60 in English. Express his marks as a percentage. Did he score more than 85%?
Answer:
90%, yes
Question 2.
A packet of cereal weighs 500g. Sugar makes up 12% of its weight. Find the weight of sugar in the packet.
Answer:
60 g
Question 3.
The price of a pair of shoes was ₹1,200 last year. This year it increased to ₹1,500. Find the percentage increase in price.
Answer:
25 %
Question 4.
Ritu bought a mixer grinder for ₹ 3,200. After one year, its value depreciated by 15%. Find its value after one year.
Answer:
₹ 2720