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ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 7 Percentage Check Your Progress

Question 1.
Convert \(\frac{7}{24}\) into a percentage correct to foursignificant figures.
Solution:

Question 2.
Express 750 mL as a percentage of 4 litres.
Solution:

Question 3.
A football team won 9 matches out of the total number of matches they played. If their win percentage was 45, then how many matches did they play in all?
Solution:

Question 4.
In a straight student election, Rahul got 66% of the votes polled. If the defeated student got 187 votes, find the total number of votes polled.
Solution:

Question 5.
36 kg of gunpowder contains 27 kg nitre, 5.4 kg charcoal and rest sulphur. Find the percentage content of sulphur in the gunpowder.
Solution:

Question 6.
75% of the students in a class passed an exam. If 2 more students had passed the exam. 80% would have been successful. How many students are there in the class ?
Solution:

Question 7.
The monthly salary of a school teacher in 2007 was ₹12000. It increased by 10% in 2008 and again by 10% in 2009. What is his salary in 2009?
Solution:

Question 8.
Price of a commodity decreased by 10% last year and increased by 20% this year. Find the percentage change in two years.
Solution:

Question 9.
A shop gives a 15% discount. What would the sale price of each of these be?
(i) A dress marked at ₹150
(ii) A pair of shoes marked at ₹800.
Solution:

Question 10.
A refrigerator marked at ₹18000 is available for ₹17100. Find the discount given and the discount percent.
Solution:

Question 11.
Ramu purchased 20 parrots at ₹30 each. Two parrots flew away and Ramu sold the rest of the parrots at ₹40 each. Calculate the profit or loss percentage of Ramu.
Solution:

Question 12.
Reena bought two tables for ₹ 1800 each. She sold one at a loss of 8% and the other at a profit of 12%. Find the selling price of each. Also, find out the total profit or loss.
Solution:

Question 13.
Ajit bought an old car ₹78000. He spent ₹2000 on repairs and repainting the car. He sold the car to Anju at a gain of 15%. Anju sold it to Anthony at a loss of 5%. What did the car cost to Anthony?
Solution:

Question 14.
Gaurav sold an article at a profit of 12%. Had it been sold for ₹16 more, the profit would have been 20%. Find the C.P. of the article.
Solution:

Question 15.
A shopkeeper allows 8% discount on his goods and still earns a profit of 15%. If an article is sold for ₹460, find :
(i) the marked price
(ii) the cost price.
Solution:

Question 16.
Rajesh bought an A.C. for ₹38500 including 10% VAT. Find the price ofA.C. before VAT was added.
Solution:

Question 17.
A DVD player is marked for ₹3000. The shopkeeper offers 10% discount on it. If VAT is received 8%. Find the amount paid by the customer.
Solution:

ML Aggarwal Class 8 Solutions for ICSE Maths

ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 7 Percentage Objective Type Questions

Mental Maths
Question 1.
Fill in the blanks:
(i) The percentage is the numerator of a fraction with denominator …………..
(ii) 15% of ………….. is 135.
(iii) \(\frac{3}{4}\) = ………..%
(iv) 50 paise = ………….. % of 8 rupees.
(v) A shopkeeper earns a profit if S.P. is ………….. than C.P.
(vi) Loss or profit % is always calculated on ………….. price.
(vii) The additional expenses on transportation, labour, repairing etc. are called …………..expenses.
(viii)Amount deducted from the marked price of an article is called ……..
(ix) Discount = Marked price – ………….. price.
(x) These days, sales tax is known as …………..
Solution:

Question 2.
State whether the following statements are true (T) or false (F):
(i) Discount is always calculated on the marked price.
(ii) Two successive discounts of 20% and 20% are equivalent to a single discount of 40%.
(iii) Overheads are always added to the original cost to get the total cost.
(iv) If S.P. is less than C.P. then shopkeeper suffers a loss.
(v) Sales tax is always calculated on the selling price.
Solution:

Multiple Choice Questions
Choose the correct answer from the given four options (3 to 18):
Question 3.
\(3 \frac{1}{8}\) % of 75 kg is equal to

Solution:

Question 4.
\(2 \frac{1}{12}\) is equivalent to

Solution:

Question 5.
\(1 \frac{11}{16}\) is equivalent to
(a) 168.75%
(b) 169.75%
(c) 170.75%
(d) 167.75%
Solution:

Question 6.
21 : 80 is equivalent to
(a) 26%
(b) 26.50%
(c) 26.75%
(d) 26.25%
Solution:

Question 7.
If 5% of a number is 42, then the number is
(a) 800
(b) 820
(c) 840
(d) 860
Solution:

Question 8.
What % of 150 is 30?
(a) 50%
(b) 10%
(c) 15%
(d) 20%
Solution:

Question 9.
A number increased by 25% gives 155. The number is
(a) 132
(b) 128
(c) 124
(d) 120
Solution:

Question 10.
Naman buys a game for ₹60 and sells it for ₹75, his profit % is
(a) 15%
(b) 20%
(c) 25%
(d) 30%
Solution:

Question 11.
Cost price of a watch is ₹680. If Rishabh sells it at a profit of 35%, then S.P. is
(a) ₹918
(b) ₹919
(c) ₹920
(d) ₹921
Solution:

Question 12.
On selling an article for ₹ 150, Renu gains ₹30. Her gain percentage is
(a) 15%
(b) 20%
(c) 25%
(d) 30%
Solution:

Question 13.
If the cost price of 5 articles is equal to the selling price of 6 articles, then there is
(a) gain
(b) loss
(c) no gain no loss
(d) none of these
Solution:

Question 14.
Marked price of an article is ₹675. If it is sold at a discount of 20%, then S.P. is
(a) ₹540
(b) ₹525
(c) ₹510
(d) ₹500
Solution:

Question 15.
A jacket is marked for ₹2590. If the S.P. of the jacket is ₹2331, then discount % is
(a) 5%
(b) 10%
(c) 15%
(d) 20%
Solution:

Question 16.
Marked price of a showpiece is ₹950. S.P. of showpiece after two successive discounts of 10% and 10% is
(a) ₹ 769.50
(b) ₹ 760
(c) ₹ 855
(d) None of these.
Solution:

Question 17.
S.P. of a video game is ₹749 including 7% VAT. The original price of a video game is
(a) ₹801.43
(b) ₹742
(c) ₹700
(d) None of these
Solution:

Question 18.
List price of an article is ₹1050. If 6% sales tax is charged, then bill amount is
(a) ₹1056
(b) ₹1113
(c) ₹1131
(d) ₹1311
Solution:

Value Based Questions
Question 1.
Out of 500 students in a school, 60% of students read Hindi Newspaper, 30% of students read English Newspaper and remaining students do not read any newspaper. Find
(i) What % of students do not read any newspaper?
(ii) Number of students who read Hindi newspaper.
(iii) Number of students who read English newspaper.
Is reading the newspaper a good habit? What are the advantages of the reading newspaper?
Solution:

Question 2.
In an exam at least 35% marks are required to pass the exam. Ramesh uses unfair means and tries to pass the exam but fails by 15 marks. If he scored 160 marks, find the maximum marks.
Is using unfair means in the exam is good? Why should we not use unfair means?
Solution:

Question 3.
A shopkeeper was involved in tax evasion. To save sales tax he never gives receipts to his customers. He sold an article for ₹550 including 10% VAT. Find the amount of VAT not paid by him to the Government. Is tax evasion correct? Why should we pay tax? What measures should we adopt to stop tax evasions?
Solution:

Higher Order Thinking Skills (Hots)
Question 1.
Marked price of an article is ₹2860 and rate of VAT is 8%. A shopkeeper allows a discount of 20% and still makes a profit of 10%. If he spent 4% as overheads, then find the original cost price of the article and final selling price including VAT.
Solution:

ML Aggarwal Class 8 Solutions for ICSE Maths

ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 7 Percentage Ex 7.4

Question 1.
Find the buying price of each of the following when 5% S.T. is added on the purchase of
(i) a towel of ₹50
(ii) 5 kg of flour at ₹15 per kg.
Solution:

Question 2.
If 8% VAT is included in the prices, find the original price of
(i) a TV bought for ₹ 13500
(ii) a shampoo bottle bought for ₹ 180.
Solution:

Question 3.
Utkarsh bought an AC for ₹34992 including a VAT of 8%. Find the price of AC before VAT was added.
Solution:

Question 4.
Gaurav bought a shirt for ₹ 1296 including VAT. If the original price of the shirt is ₹ 1 200, find the rate of VAT.
Solution:

Question 5.
Anjana buys a purse for ₹523.80 including 8% VAT. Find the new selling price of the purse if VAT increases to 10%.
Solution:

Question 6.
A wall hanging is marked for ₹4800. The shopkeeper offers 10% discount on it. If VAT is received 8% from the customer, find the amount paid by the customer to purchase the wall hanging.
Solution:

Question 7.
Amit goes to a shop to buy a washing machine. The marked price of the washing machine is ₹ 10900 excluding9% VAT. Amit bargains with a shopkeeper and convinces him for ₹10900 including VAT as the final cost of the washing machine. Find the amount reduced by the shopkeeper.
Solution:

ML Aggarwal Class 8 Solutions for ICSE Maths

ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 7 Percentage Ex 7.3

Question 1.
Find the discount and the selling price, when:
(i) the marked price = ₹575, discount = 12%
(ii) the printed price = ₹12750, discount = \(8 \frac{1}{3}\)%
Solution:

Question 2.
Find the discount and the discount percentage, when :
(i) marked price = ₹780, selling price = ₹721·50
(ii) advertised price = ₹28500, selling price = ₹24510
Solution:

Question 3.
A notebook is marked at ₹30. Find the price a student pays for a dozen notebooks if he gets 15% discount.
Solution:

Question 4.
A dealer gave 9% discount on an electric fan and charges ₹ 728 from the customer. Find the marked price of the fan.
Solution:

Question 5.
The list price of an article is ₹800 and a dealer is selling it at a discount of 20%. Find :
(i) the selling price of the article.
(ii) the cost price of the article if he makes 25% profit on selling it.
Solution:

Question 6.
A shopkeeper marks his goods at such a price that would give him a profit of 10% after allowing a discount of 12%. If an article is marked at ₹2250, find its :
(i) selling price
(ii) cost price.
Solution:

Question 7.
A shopkeeper purchased a calculator for ₹650. He sells it at a discount of 20% and still makes a profit of 20%. Find :
(i) the selling price
(ii) marked price
Solution:

Question 8.
A shopkeeper buys a dinner set for ₹ 1200 and marks it 80% above the cost price. If he gives 15% discount on it, find :
(i) the marked price
(ii) the selling price
(iii) his profit percentage.
Solution:

Question 9.
The cost price of an article is ₹1600, which is 20% below the marked price. If the article is sold at a discount of 16%, find :
(i) the marked price
(ii) the selling price
(iii) profit percentage.
Solution:

Question 10.
A shopkeeper allows 20% discount on his goods and still earns a profit of 20%. If an article is sold for ₹360, find:
(i) the marked price
(ii) tine cost price.
Solution:

Question 11.
The printed price of a refrigerator is ₹28600. A dealer allows two successive discount of 10% and 5%. Find the price which a customer has to pay for the refrigerator.
Solution:

Question 12.
Two dealers have marked an article at the same price. The first dealer allows two successive discounts of 15% and 5%. The other allows for a discount of 20% which is the better offer?
Solution:

Question 13.
Find a single discount equivalent to two successive discounts of 30% and 10%.
Solution:

ML Aggarwal Class 8 Solutions for ICSE Maths

ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 7 Percentage Ex 7.2

Question 1.
Find the profit or loss percentage, when:
(i) C.P. = ₹400, S.P. = ₹468
(ii) C.P. = ₹ 13600, S.P. = ₹12104
Solution:

Question 2.
By selling an article for ₹1636·25, a dealer gains ₹96·25. Find his gain per cent.
Solution:

Question 3.
By selling an article for ₹770, a man incurs a loss of ₹110. Find his loss percentage.
Solution:

Question 4.
Rashida bought 25 dozen eggs at the rate of ₹9.60 per dozen. 30 eggs were broken in the transaction and she sold the remaining eggs at one rupee each. Find her gain or loss percentage.
Solution:

Question 5.
The cost of an article was ₹20000 and ₹1400 were spent on its repairs. If it is sold for a profit of 20%, find the selling price of the article.
Solution:

Question 6.
A shopkeeper buys 200 bicycles at ₹1200 per bicycle. He spends ₹30 per bicycle on transportation. He also spends ₹4000 on advertising. Then he sells all the bicycles at ₹1350 per piece. Find his profit or loss. Also calculate it as a percentage.
Solution:

Question 7.
The cost price of an article is 90% of its selling price. Find his profit percentage.
Solution:

Question 8.
Rao bought notebooks at the rate of 4 for ₹35 and sold them at the rate of 5 for ₹58. Calculate
(i) his gain percentage.
(ii) the number of notebooks he should sell to earn a profit of ₹171.
Solution:

Question 9.
A vendor buys bananas at 3 for a rupee and sells at 4 for a rupee. Find his profit or loss percentage.
Solution:

Question 10.
A shopkeeper buys a certain number of pens. If the selling price of 5 pens is equal to the cost price of 7 Pens, find his profit or loss percentage.
Solution:

Question 11.
Find the selling price, when :
(i) Cost price = ₹2360, Profit = 8%
(ii) Cost price = ₹380, Loss = 7·5%
Solution:

Question 12.
A dealer bought a number of eggs at ₹18 a dozen and sold them at 50% profit. Find the selling price per egg.
Solution:

Question 13.
Mr Ghosh purchased wristwatches worth ₹60000. He sold one-third of them at a profit of 30%, one-third at a profit of 20% and remaining at a loss of 5%. Calculate his overall profit or loss percentage.
Solution:

Question 14.
A laptop and a mobile phone were bought for ₹40000 and ₹24000 respectively. The shopkeeper made a profit of 8% on the laptop and a loss of 12% on a mobile phone. Find his gain or loss per cent on the whole transaction.
Solution:

Question 15.
Salman bought 40 chairs at ₹175 each fourth of them at a loss of 8%. At what price each must he sell the remaining chairs so as to gain 10% on the whole deal?
Solution:

Question 16.
A shopkeeper sold two electronic gadgets for ₹44000 each. The shopkeeper made a loss of 12% on one and a profit of 10% on the other. Find his overall gain or loss.
Solution:

Question 17.
The manufacturing price of a T.V. set is ₹12000. The company sold it to a dealer at 20% profit and the dealer sold it to a customer at 12·5% profit. Find the price which the customer has to pay.
Solution:

Question 18.
Find the cost price, when :
(i) selling Price = ₹450, loss = 10%
(ii) selling Price = ₹690, profit = 15%
Solution:

Question 19.
By selling an almirah for ₹3920, a shopkeeper would gain 12%. If it is sold for ₹4375, find his gain or loss, percentage.
Solution:

Question 20.
By selling a bicycle at ₹1334, a shopkeeper would suffer a loss of 8%. At how much amount should he sell it to make a profit of \(12 \frac{1}{2}\)%?
Solution:

Question 21.
By selling a tie for ₹252, a shopkeeper gains 5%. At what price should he sell the tie to gain 35 %?
Solution:

Question 22.
A shopkeeper sells a bag at a 12% profit. If he had sold it for ₹39 more, he would have made 18% profit. Find the cost price of the bag for the shopkeeper.
Solution:

Question 23.
A shopkeeper sells a sweater at a loss of 5%. If he had sold it for ₹260 more, he would have made a profit of 15%. Calculate the purchase price of the sweater.
Solution:

Question 24.
Janki sold her leather purse at 8% loss. If she had sold it for ₹ 150 more, she would have made 12% profit. Find the selling price of the purse.
Solution:

ML Aggarwal Class 8 Solutions for ICSE Maths

ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 7 Percentage Ex 7.1

Question 1.
Express the following percentages as fractions:
(i) 356%
(ii) \(2 \frac{1}{2}\)%
(iii) \(16 \frac{2}{2}\)%
Solution:

Question 2.
Express the following fractions as percentages:

Solution:

Question 3.
Express the following fractions as decimals. Then express the decimals as percentages:

Solution:

Question 4.
Express the following fractions as decimals correct to four decimal places. Then express the decimals as percentages:

Solution:

Question 5.
Express the following ratios as percentages:
(i) 17 : 20
(ii) 13 : 18
(iii) 93 : 80
Solution:

Question 6.
Express the following percentages as decimals:
(i) 20%
(ii) 2%
(iii) \(3 \frac{1}{4}\)%
Solution:

Question 7.
Find the value of:
(i) 27% of ₹50
(ii) \(6 \frac{1}{4}\)% of 25 kg
Solution:

Question 8.
What per cent is :
(i) 300 g of 2 kg
(ii) ₹7·50 of ₹6
Solution:

Question 9.
What per cent of:
(i) 50 kg is 65 kg
(ii) ₹9 is ₹4
Solution:

Question 10.
(i) If \(16 \frac{2}{3}\)% of a number is 25, find the number.
(ii) If 13·25% of a number is 159, find the number.
Solution:

Question 11.
(i) Increase the number 60 by 30%
(ii) Decrease the number 750 by 10%
Solution:

Question 12.
(i) What number when increased by 15% becomes 299?
(ii) On decreasing the number by 18%, it becomes 697. Find the number.
Solution:

Question 13.
Mr Khanna spent 83% of his salary and saved ₹1870. Calculate his monthly salary.
Solution:

Question 14.
In school, 38% of the students are girls. If the number of boys is 1023, find the total strength of the school.
Solution:

Question 15.
The price of an article increases from ₹960 to ₹1080. Find the percentage increase in the price.
Solution:

Question 16.
In a straight contest, the loser polled 42% votes and lost by 14400 votes. Find the total number of votes polled. If the total number of eligible voters was 1 lakh, find what percentage of voters did not vote.
Solution:

Question 17.
Out of 8000 candidates, 60% were boys. If 80% of the boys and 90% of the girls passed the exam, find the number of candidates who failed.
Solution:

Question 18.
In an exam, \(\frac{1}{4}\) of the students failed both in English and Maths, 35% of students failed in Maths and 30% failed in English.
(i) Find the percentage of students who failed in any of the subjects.
(ii) Find the percentage of students who passed in both subjects.
(iii) If the number of students who failed only in English was 25, find the total number of students.
Solution:

Question 19.
On increasing the price of an article by 16%, it becomes ₹1479. What was its original price?
Solution:

Question 20.
Pratibha reduced her weight by 15%. If now she weighs 59.5 kg, what was her earlier weight?
Solution:

Question 21.
In a sale, a shop reduces all its prices by 15%. Calculate:
(i) the cost of an article which was originally priced at ₹40.
(ii) the original price of an article which was sold for ₹20.40.
Solution:

Question 22.
Increase the price of ₹200 by 10% and then decrease the new price by 10%. Is the final price same as the original one ?
Solution:

Question 23.
Chandani purchased some parrots. 20% flew away and 5% died. Of the remaining, 45% were sold. Now 33 parrots remain. How many parrots had Chandani purchased?
Solution:

Question 24.
A candidate who gets 36% marks in an examination fails by 24 marks but another candidate, who gets 43% marks, gets 18 more marks than the minimum pass marks. Find the maximum marks and the percentage of pass marks.
Solution:

ML Aggarwal Class 8 Solutions for ICSE Maths

ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 6 Operation on sets Venn Diagrams Check Your Progress

Question 1.
If ξ={x : x ϵ N, r < 25} and A = {x : x is a composite number}, then find A’ in set builder from and also in roster form.
Solution:

Question 2.
If ξ = {x | x ϵ I, -5 ≤ x ≤ 5}, A = {-5, -3, 0, 3, 5} and B = {-4, -2, 0, 2, 4}, then
(i) Find A ∪ B and A ∩ B
(ii) Verify that n(A ∪ B) = n(A) + n(B) – n(A ∩ B).
(iii) Find A’ and verify that n(A) + n(A’) = n(ξ).
(iv) Find B’ and verify that n(B’) = n(ξ) – n(B)
(v) Find A ∪ A’, A ∩ A’, B ∪ B’ and B ∩ B’.
(vi) Find (A ∪ B)’ and A’ ∩ B’. Are they equal ?
(vii) Find (A ∩ B)’ and A’ ∪ B’. Are they equal ?
Solution:

Question 3.
If ξ = {x | x ϵ N, x ≤ 12}, A = {prime numbers} and B = {odd numbers}, then
(i) Find A ∪ B and A ∩ B.
(ii) Verify that n(A ∪ B) + n(A ∩ B) = n(A) + n(B).
(iii) Find A’ and B’.
(iv) Find (A ∪ B)’ and verify that n(A ∪ B) + n(A ∪ B)’ = n(ξ).
(v) Find (A ∩ B)’ and A’ ∪ B’. Are they equal ?
Solution:

Question 4.
If ξ = {x : x ϵ N, x ≤ 12}, A= {x : x ≥ 7} and B = {x : 4 < x < 10}. Find :
(i) A’
(ii) B’
(iii) A ∪ B
(iv) A ∩ B
(v) A – B
(vi) B – A
(vii) (A ∪ B)’
(viii) A’ ∩ B’
Also verify that:
(i) (A ∪ B)’ = A’ ∩ B’
(ii) A – B = A ∩ B’
(iii) n(A ∪ B) + n((A ∪ B)’) = n(ξ)
(iv) n(A ∪ B) = n(A – B) + n(B – A) + n(A ∩ B).
Solution:

Question 5.
Given A = {students who like cricket} and B = {students who like tennis}; n(A) = 20, n(B) = 15 and n(A ∩ B)= 5.
Illustrate this through a Venn diagram. Hence find n(A ∪ B).
Solution:

Question 6.
If n(ξ) = 50, n(A) = 15, n(B) = 13 and n(A ∩ B) = 10. Find n(A’), n(B’) and n(A ∪ B).
Solution:

Question 7.
If n(ξ) = 60, n(A) = 35, n(B’) = 36 and n((A ∩ B)’) = 51, find :
(i) n(B)
(ii) n(A ∩ B)
(iii) n(A ∪ B)
(iv) n(A – B)
Solution:

Question 8.
In a city, 50% of people read newspaper A, 45% read newspaper B, and 25% read neither A nor B. What percentage of people read both the newspapers A as well as B?
Solution:

ML Aggarwal Class 8 Solutions for ICSE Maths

ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 6 Operation on sets Venn Diagrams Objective Type Questions

Mental Maths
Question 1.
Fill in the blanks:
(i) If A, B are two sets, then A ∪ B = …………..
(ii) If A, B are two sets, then A ∩ B = …………..
(iii) If A, B are two sets, then A – B = …………..
(iv) A and B are disjoint sets if and only if A ∩ B = …………..
(v) A and B are overlapping sets if and only if A ∩ B = …………..
(vi) The set {x: x ϵ W, x < 3} in the roster form = …………..
(vii) If A is any set, then A ∪ ϕ = and A ∪ ξ = …………..
(viii) If ξ = {all digits in our number system] and A ={1,2, 3, 4, 5}, then A’= …………..
(ix) If A is any set and A’ is its complement, then A ∪ A’ = and A ∩ A’ = …………..
Solution:

Question 2.
State whether the following statements are true (T) or false (F):
(i) If ξ is the universal set and A is any set, then A’ = {x; x ϵ ξ and r ∉ A}.
(ii) If A = {0,1,2,3,4, 5} and B = {0,3, 5, 7}, then A ∩ B = B.
(in) If A= {0,1, 2,3,4, 5} and B = {0,3,5,7}, then A ∪ B=A.
(iv) If ξ = {all digits in our number system}, A = {multiples of 2} and B = {multiples of 3}, then A ∩ B = {6}.
Solution:

Multiple Choice Questions
Choose the correct answer from the given four options (3 to 12):
Question 3.
If A = {x | x is a colour of rainbow} and B = {white, red, green}, then A ∩ B is
(a) B
(b) {green}
(c) {red}
(d) {green, red}
Solution:

Question 4.
If P = {-1, 0, 1, 2, 5} and Q = {3, 5, 7}, then P ∪ Q is
(a) {5}
(b) {-1, 0, 1, 2, 3, 7}
(c) {-1, 0, 1, 2, 3, 5, 7}
(d) none of these
Solution:

Question 5.
If A and B are two sets, then A – B is defined as
(a) {x |x ϵ A or x ϵ B}
(b) {x | x ϵ A and x ϵ B}
(c) {x | x ϵ A and x ∉ B}
(d) {x | x ϵ B and x ∉ A}
Solution:

Question 6.
If A is any set, then A ∪ ϕ is
(a) A
(b) ϕ
(c) 2,
(d) none of these
Solution:

Question 7.
A ∩ ξ is same as
(a) A
(b) ϕ
(c) A’
(d) ξ
Solution:

Question 8.
If ξ = W and A = {x | x ϵ W and x ≤ 10}, then A’ is
(a) ϕ
(b) {x | x ϵ W and 0 ≤ x ≤ 10}
(c) {x | x ϵ W and x ≤ 10}
(d) {x | x ϵ W and x ≥ 11}
Solution:

Question 9.
If ξ= {x | x ϵ W, x ≤ 12}, A – {x | x is a multiple of 3} and B = {x | x is a multiple of 4}, then A ∩ B is
(a) ϕ
(b) {0}
(c) {12}
(d) {0, 12}
Solution:

Question 10.
If ξ = (all digits in our number system}, A = {x | x is prime} and B = {x | x is even}, then B – A is
(a) {4, 6, 8}
(b) {0, 4, 6, 8}
(c) {3, 5, 7}
(d) {2}
Solution:

Question 11.
If A and B are two sets such that n(A) = 22, n(B) = 18 and n(A ∪ B) = 35, then n(A ∩ B)
(a) 4
(b) 5
(c) 15
(d) 75
Solution:

Question 12.
In a town of 840 persons, 450 persons read Hindi, 300 read English and 200 read both. Then the number of person who read neither is
(a) 180
(b) 210
(c) 260
(d) 290
Solution:

ML Aggarwal Class 8 Solutions for ICSE Maths

ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 6 Operation on Sets Venn Diagrams Ex 6.2

Question 1.
From the adjoining Venn diagram, find the following sets :
(i) A
(ii) B
(iii) ξ
(iv) A’
(v) B’
(vi) A ∪ B
(vii) A ∩ B
(viii) (A ∪ B)’
(ix) (A ∩ B)’

Solution:

Question 2.
From the adjoining Venn diagram, find the following sets :

(i) P
(ii) Q
(iii) ξ
(iv) P’
(v) Q’
(vi) P ∪ Q
(vii) P ∩ Q
(viii) (P ∪ Q)’
(ix) (P ∩ Q)’
Solution:

Question 3.
From the adjoining Venn diagram, find the following sets :
(i) ξ
(ii) A ∩ B
(iii) A ∩ B ∩ C
(iv) C’
(v) A – C
(vi) B – C
(vii) C – B
(viii) (A ∪ B)’
(ix) (A ∪ B ∪ C)’

Solution:

Question 4.
Draw Venn diagrams to show the relationship between the following pairs of sets :
(i) A = {x | x ϵ N, x = 2n, n ≤ 5} and
B = {x | x ϵ W, x = 4n, n < 5}
(ii) A = {prime factors of 42} and
B = {prime factors of 60}
(iii) P = {x | x ϵ W, x < 10} and
Q = {prime factors of 210}
Solution:

Question 5.
Draw a Venn diagram to illustrate the following information:
n (A) = 22, n (B) = 18 and n (A ∩ B) = 5.
Hence find:
(i) n (A ∩ B)
(ii) n (A – B)
(iii) n (B – A)
Solution:

Question 6.
Draw a Venn diagram to illustrate the following information: n (A) = 25, n (B) = 16, n (A ∩ B) = 6 and n ((A ∪ B)’) = 5
Hence find:
(i) n (A ∪ B)
(ii) n (ξ)
(iii) n (A – B)
(iv) n (B – A)
Solution:

Question 7.
Given n(ξ) = 25, n (A’) = 7, n (B) = 10 and B ⊂ A. Draw a Venn diagram to illustrate this information. Hence, find the cardinal number of the set A – B.
Solution:

Question 8.
In a group of 50 boys, 20 play only cricket, 12 play only football and 5 boys play both the games. Draw a Venn diagram and find the number of boys who play
(i) at least one of the two games cricket or football.
(ii) neither cricket nor football.
Solution:

Question 9.
In a group of 40 students, 26 students like orange but not banana, while 32 students like orange. If all the students like atleast one of the two fruits, find the number of students who like
(i) both orange and banana
(ii) only banana.
Draw a Venn diagram to represent the data.
Solution:

Question 10.
In a group of 60 persons, 45 speak Bengali, 28 speak English and all the persons speak atleast one language. Find how many people speak both Bengali and English. Draw a Venn diagram.
Solution:

ML Aggarwal Class 8 Solutions for ICSE Maths

ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 6 Operation on sets Venn Diagrams Ex 6.1

Question 1.
If A = {0, 1, 2, 3, …….., 8}, B = {3, 5, 7, 9, 11} and C = {0, 5, 10, 20}, find
(i) A ∪ B
(ii) A ∪ C
(iii) B ∪ C
(iv) A ∩ B
(v) A ∩ C
(vi) B ∩ C
Also find the cardinal number of the sets B ∪ C, A ∪ B, A ∩ C and B ∩ C.
Solution:

Question 2.
Find A’ when
(i) A= {0, 1, 4, 7} and E, = {x | x ϵ W, x ≤ 10}
(ii) A = {consonants} and ξ = {alphabets of English}
(iii) A = boys in class VIII of all schools in Bengaluru} and ξ = {students in class VIII of all schools in Bengaluru}
(iv) A = {letters of KALKA} and ξ = {letters of KOLKATA}
(v) A = {odd natural numbers} and ξ = {whole numbers}.
Solution:

Question 3.
If A {x : x ϵ N and 3 < x < 1} and B = {x : x ϵ Wand x ≤ 4}, find
(i) A ∪ B
(ii) A ∩ B
(iii) A – B
(iv) B – A
Solution:

Question 4.
If P = {x : x ϵ W and x < 6} and Q = {x : x ϵ N and 4 ≤ x ≤ 9}, find
(i) P ∪ Q
(ii) P ∩ Q
(iii) P – Q
(iv) Q – P
Is P ∪ Q a proper superset of P ∩ Q ?
Solution:

Question 5.
If A = (letters of word INTEGRITY) and B = (letters of word RECKONING), find
(i) A ∪ B
(ii) A ∩ B
(iii) A – B
(iv) B – A
Also verify that:
(a) n(A ∪ B) = n(A) + n(B) – n(A ∩ B)
(b) n(A – B) = n(A ∪ B) – n(B)
= n(A) – n(A ∪ B)
(c) n(B – A) = n(A ∪ B) – n(A)
= n(B) – n(A ∩ B)
(d) n(A ∪ B) = n(A – B) + n(B – A) + n(A ∩ B).
Solution:

Question 6.
If ξ = {natural numbers between 10 and 40}
A = {multiples of 5} and
B = {multiples of 6}, then
(i) find A ∪ B and A ∩ B
(ii) verify that
n(A ∪ B) = B (A) + n(B) – n(A ∩ B).
Solution:

Question 7.
If ξ ={1,2, 3, …. 9}, A = {1, 2, 3, 4, 6, 7, 8} and B = {4, 6, 8}, then find.
(i) A’
(ii) B’
(iii) A ∪ B
(iv) A ∩ B
(v) A – B
(vi) B – A
(vii) (A ∩ B)’
(viii) A’ ∪ B’
Also verify that:
(a) (A ∩ B)’ = A’ ∪ B’
(b) n(A) + n(A’) = n(ξ)
(c) n(A ∩ B) + n((A ∩ B)’) = n(ξ)
(d) n(A – B) + n(B – A) + n(A ∩ B)
= n(A ∪ B).
Solution:

Question 8.
If 4 = {x : x ϵ W, x ≤ 10}, A. = {x : x ≥ 5} and B = {x : 3 ≤ x < 8}, then verify that:
(i) (A ∪ B)’ = A’ ∩ B’
(ii) (A ∩ B)’= A’ ∪ B’
(iii) A – B = A ∩ B’
(iv) B – A = B ∩ A’
Solution:

Question 9.
If n(A) = 20, n(B) = 16 and n(A ∪ B) = 30, find n(A ∩ B).
Solution:

Question 10.
If n ξ = 20 and n(A’) = 7, then find n(A).
Solution:

Question 11.
If n(ξ) = 40, n(A) = 20, n(B’) = 16 and n(A ∪ B) = 32, then find n(B) and n(A ∩ B).
Solution:

Question 12.
If n(ξ) = 32, n(A) = 20, n(B) = 16 and n((A ∪ B)’) = 4, find :
(i) n(A ∪ B)
(ii) n(A ∩ B)
(iii) n(A – B)
Solution:

Question 13.
If n(ξ) = 40, n(A’) = 15, n(B) = 12 and n((A ∩ B)’) = 32, find :
(i) n(A)
(ii) n(B’)
(iii) n(A ∩ B)
(iv) n(A ∪ B)
(v) n(A – B)
(vi) n(B – A)
Solution:

Question 14.
If n(A – B) = 12, n(B – A) = 16 and n(A ∩ B) = 5, find:
(i) n(A)
(ii) n(B)
(iii) n(A ∪ B)
Solution:

ML Aggarwal Class 8 Solutions for ICSE Maths

ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 2 Exponents and Powers Check Your Progress

Question 1.
Evaluate:

Solution:

Question 2.
Simplify:

Solution:

Question 3.
Find the multiplicative inverse of \(\left(\frac{125}{27}\right)^{\frac{-2}{3}}\)
Solution:

Question 4.
Simplify and write in exponential form:

Solution:

Question 5.
Simplify: \(\frac{5^{n+2}-6+5^{n+1}}{13 \times 5^{n}-2 \times 5^{n+1}}\)
Solution:

Question 6.
Prove that (a + b)^-1 (a^-1 + b^-1) = (ab)^-1.
Solution:

Question 7.
Find the value of x for which

Solution:

Question 8.
If \(\frac{2^{-n} \times 8^{2 n+1} \times 16^{2 n}}{4^{3 n}}=\frac{1}{16}\), find the value of n.
Solution:

Question 9.
By what number should \(\left[\left(\frac{-5}{2}\right)^{3}\right]^{-3}\) be multiplied to get \(\left(\frac{-2}{5}\right)^{5}\)?
Solution:

Question 10.
By what number should \(\left(\frac{-3}{2}\right)^{-4}\) be divided to get \(\left(\frac{-2}{3}\right)^{3}\)?
Solution:

Question 11.
Express the following numbers in standard form:
(i) 0.0000000003904
(ii) 12730000000000
Solution:

Question 12.
Express the following numbers in the usual form:
(i) 5.73 × 10^-11
(ii) 3.895 × 10¹⁵.
Solution:

Question 13.
If \(\left(\frac{9}{4}\right)^{-4} \times\left(\frac{2}{3}\right)^{3}=\left(\frac{p}{q}\right)^{11}\), then find the value of \(\left(\frac{p}{q}\right)^{-2}\).
Solution:

Question 14.
Mass of the Earth is 5.97 × 10²⁴ kg and mass of the Moon is 7.35 × 10²² kg. What is the difference of their masses?
Solution:

ML Aggarwal Class 8 Solutions for ICSE Maths