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Important Questions Class 8 Maths Part 2 Chapter 1 Fractions in Disguise

Fractions in Disguise is Chapter 1 of the Class 8 Maths book Ganita Prakash Part 2. It shows how fractions appear in disguise as percentages and decimals. Students convert between fractions, decimals and percentages, and solve problems on profit, loss, discount and simple interest.

This page gives 12 important questions from Class 8 Maths Part 2 Chapter 1 Fractions in Disguise with step-by-step answers prepared by Extramarks experts. The questions cover converting fractions to percentages, reading graphs, percentage increase and decrease, discount deals, and profit and loss. Solve each question on paper first and then check your working with the answer.

Q1. In a school survey, it was found that

Class 8 Maths Part 2 Ch 1 Q1

percentage of students who prefer outdoor games and find the final percentage.

Answer:

Class 8 Maths Part 2 Ch 1 Q1 answer

Q2. Express 58% as a fraction and as a decimal.

Answer: To convert a percentage into a fraction or a decimal, we divide it by 100.

Class 8 Maths Part 2 Ch 1 Q2 answer

Q3. Out of 30 students in a hostel, 8 are going to market, 20 are going to watch T.V. and the rest of the students are studying. Convert all of them into percentages.

Answer: Total students in the hostel = 30 and the number of students going to market = 8

Class 8 Maths Part 2 Ch 1 Q3 answer

The number of students watching T.V. = 20

Class 8 Maths Part 2 Ch 1 Q3 answer

The rest of the students are studying.

Class 8 Maths Part 2 Ch 1 Q3 answer

Q4. Fill in the blanks:

(i) 3 is ____ % of 300.

(ii) ____ is 40% of 4.

(iii) 40 is 80% of ____

Answer:

Class 8 Maths Part 2 Ch 1 Q4 answer

Q5. In a school, 15 of the 80 students come to school by walking. What percentage of the students come by walking?

Answer:

Class 8 Maths Part 2 Ch 1 Q5 answer

Q6. Look at the following graph.

Class 8 Maths Part 2 Ch 1 Q6

Based on the graph, which of the following statements are valid?

(i) People in their twenties are the most computer-literate among all age groups.

(ii) Women lag 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.

Answer: (i) True

(ii) True

(iii) True

(iv) False

(v) True

(vi) False

Q7. 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%?

Answer: Number of people in the room = 100

Number of left-handers = 99% of 100 = 99, so the number of right-handers = 1

Let x left-handers leave. Then the left-handers become 98% of the people left in the room.

Class 8 Maths Part 2 Ch 1 Q7 answer

⇒ 100(99 – x) = 98(100 – x)

⇒ 9900 – 100x = 9800 – 98x

⇒ 9900 – 9800 = 100x – 98x

⇒ 2x = 100 ⇒ x = 50

∴ 50 left-handers must leave the room.

Q8. 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?

Answer:

Class 8 Maths Part 2 Ch 1 Q8 answer

Cheapest to costliest: A, B, C.

Class 8 Maths Part 2 Ch 1 Q8 answer

(iii) To buy 4 items, we choose Shop A. We pay for 2 items and the other 2 are free.

Q9. 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.

Class 8 Maths Part 2 Ch 1 Q9

Answer:

Class 8 Maths Part 2 Ch 1 Q9 answer

Verification: 45.5 + 15.6 + 1.95 + 1.95 = 65 g (approximately)

Q10. If the length of a rectangle is increased by 10% and the area is unchanged, by what percentage (exactly) does the breadth decrease?

Answer:

Class 8 Maths Part 2 Ch 1 Q10 answer

Q11. 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?

Answer: Let the bus fare 2 years ago be ₹ 100.

Present bus fare = ₹ 100 × 1.03 × 1.04 = ₹ 107.12

Increase = ₹ 7.12 on ₹ 100

Class 8 Maths Part 2 Ch 1 Q11 answer

So, the overall increase in the last 2 years is 7.12%.

Q12. 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?

Answer: SP of 3 pencils = CP of 5 pencils

Let this amount be ₹ 15 (a common multiple of 3 and 5).

Then SP of 1 pencil = ₹ 15 ÷ 3 = ₹ 5 and CP of 1 pencil = ₹ 15 ÷ 5 = ₹ 3

Since SP > CP, he makes a profit. Profit = ₹ 5 – ₹ 3 = ₹ 2

Profit % = (2 ÷ 3) × 100 = 66.67%

Related Study Material on Extramarks

Q.1 A washing machine was sold for 5760 after giving successive discounts of 15% and 10% respectively. What was the marked price

Marks:4
Ans

$\begin{array}{l} Selling price of washing machine = 5760 \\ Two successive discounts are 15% and 10%. \\ Let marked price of washing machine = x \\ S . P . of washing machine after first discount = x (\frac{100 ˆ’ 15}{100}) \\ = \frac{85 x}{100} \\ = \frac{17 x}{20} \\ S . P . of washing machine after second discount = \frac{17 x}{20} (\frac{100 ˆ’ 10}{100}) \\ = \frac{17 x}{20} — \frac{90}{100} \\ = \frac{153 x}{200} \\ Then, according to condition \\ \frac{153 x}{200} = Rs . 5760 \\ x = 5760 — \frac{200}{153} \\ x = 7529 .40 (approx) \\ Thus, the marked price of washing machine is 7529 .40. \end{array}$

Q.2 Find the compound interest on 1,60,000 for 2 years at 10% per annum when compounded semi-annually.

Marks:2
Ans

$\begin{array}{l} Principal = 160000, \\ rate = 10% per annum = 5% per half year \\ Time = 2 years = 4 half years. \\ Amount = \{160000 — {(1 + \frac{5}{100})}^{4}\} \\ = 160000 — \frac{21}{20} — \frac{21}{20} — \frac{21}{20} — \frac{21}{20} \\ = 1, 94, 481 \\ Compound Interest = 1, 94, 481 ˆ’ 1, 60, 000 \\ = 34,481 \end{array}$

Q.3 Find the amount on a principal of 2000 for 2 years at 10% per annum compounded annually. Also find the compound interest.

Marks:1
Ans

$\begin{array}{l} A = P {(1 + \frac{r}{100})}^{n} \\ = 2000 {(1 + \frac{10}{100})}^{2} \\ = 2000 — \frac{110}{100} — \frac{110}{100} = 2420 \\ Amount = 2420 \\ Compound Interest = Amount - Principal \\ = 2420 - 2000 = 420 \end{array}$

Q.4 When 5% sale tax is added on the purchase of a bedsheet of 300, find the buying price or the cost price of the bedsheet.

Marks:1
Ans

$\begin{array}{l} 5 % of 300 is \frac{5}{100} — 300 = 15 \\ buying price of Bedsheet is 300 + 15 = 315 \end{array}$

Q.5 Rakesh bought a watch for 800 and sold it for 1000. Mukesh bought a car for 4,00,000 and sold it for 4,20,000. Who made a better sale, Rakesh or Mukesh

Marks:4
Ans

$\begin{array}{l} C.P. of watch for Rakesh = 800 \\ S.P. of watch for Rakesh = 1000 \\ Profit on watch to Rakesh = 1000 ˆ’ 800 \\ = 200 \\ Rate of Profit = \frac{200}{1000} — 100 \\ = 20 % \\ C.P. of car for Mukesh = 4,00,000 \\ S.P. of car for Mukesh = 4,20,000 \\ Profit on car for Mukesh = (4,20,000 ˆ’ 4,00,000) \\ Profit on car for Mukesh = 20, 000 \\ Rate of Profit = \frac{20, 000}{4,00,000} — 100 \\ = 5 % \\ So, Rakesh made a better sale. \end{array}$

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Important Questions for Class 8 Maths

Chapter 1 - Rational Numbers

Chapter 2 - Linear Equation in One Variable

Chapter 3 - Understanding Quadrilaterals

Chapter 4 - Practical Geometry

Chapter 5 - Data Handling

Chapter 6 - Squares and Square Roots

Chapter 7 - Cubes and Cube Roots

Chapter 9 - Algebraic Expressions and Identities

Chapter 10 - Visualising Solid Shapes

Chapter 11 - Mensuration

Chapter 12 - Exponents and Powers

Chapter 13 - Direct and Inverse Proportions

Chapter 14 - Factorisation

Chapter 15 - Introduction to Graphs

Chapter 16 - Playing with Numbers

FAQs (Frequently Asked Questions)

The most important questions come from FDP conversions, percentage of a quantity, profit and loss, discount, GST, simple interest, compound interest, and tricky percentage changes. Practise at least one question from each type.

Start by writing CP and SP. If SP is more than CP, it is profit. If SP is less than CP, it is loss. Profit % and loss % are always calculated on CP, not on SP.

Learn common FDP values first. For example, 1/2 = 0.5 = 50%, 1/4 = 0.25 = 25%, and 3/4 = 0.75 = 75%. These help solve many questions mentally.

Simple interest is calculated only on the original principal. Compound interest is calculated on the updated amount after adding previous interest. That is why compound interest becomes higher over time.

Percentage questions become tricky when the base changes. A 30% discount followed by 20% discount is not 50%. Each percentage acts on a different value, so students should write the base first.

Important Questions Class 8 Maths Part 2 Chapter 1 Fractions in Disguise