DELHI PUBLIC SCHOOL, M R NAGAR, MATHURA, REVISION ASSIGNMENTS, CLASS VIII, MATHEMATICS

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1 CHAPTER: COMPARING QUANTITIES TOPIC: RATIO, PERCENTAGE AND PERCENTAGE INCREASE/DECREASE: SET : 1 1. Rajesh decided to cycle down to his grandma s house. The house was 42 km away from his house. He cycled 14.7 km, then gave up and took a bus. What percent of the distance did he cover by bus? 2. A pot of grey paint contains black paint and white paint in the ratio 3:17. (a) What percentage of paint is black? (b) How much white paint will be required to make 3.5 l of grey paint? (c) How much black paint is required to make 10.4 l of grey paint? 3. Mr Mehra spends 30% of his monthly income on food, 10% on charity, saves 25% and is left with Rs 15,750. What is his monthly salary? Also find his monthly savings. 4. A candidate scored 25% marks in an examination and failed by 30 marks, while another candidate who scored 50% marks got 20 marks more than the minimum pass marks. Find the minimum pass marks and the maximum marks. 5. A man participated in a quiz and he attempted all the questions. He answered % of questions correctly and 7 answers were incorrect. Find how many questions he answered correctly and what the total number of questions was. 6. After a 15% increase in salary, Rajat gets Rs 51,750. Find his previous salary. 7. A number is increased by 10% and then decreased by 10% find the net increase/decrease percent. 8. Deepak earns 20% less than Neeraj. By what percent is Neeraj s earnings more than Deepak s? 9. The price of milk has increased by 20%. By what percent must Ms Sharma reduce her consumption so that her expenditure on milk does not increase? 10. Ram s earnings is 40% of Shyam s. Shyam s earning is 25% of Mohan s earning. If Mohan s earning is Rs 1,00,000, then find Ram s and Shyam s earnings. 11. An incentive amout of Rs 58,000 was divided among three salespersons X, Y and Z. X got 80% of what Y got and Y got 25% of what Z got. Find the amount each salesperson got. Also find what percentage of the incentive amount Y received. 12. Heena has 15% more sweets than Harish. By what percent is Harish s number of sweets less than that of Heena s? 13. Mona s salary is 10% more than Shruti s. How much percent is Shruti s income less than Mona s? 14. A number is increased by 20% and then decreased by 20%. Find the net increase or decrease percent. 15. The prices of pulses increased by 30%. By how much percent should Nalini reduce her consumption of pulses so that her expenditure on pulses does not change? 16. Ranit scored 62% in English, 80% in maths and 56% in SSt. If the MM in these subjects were 50, 100 and 75 respectively, find his aggregate percentage. 17. The value of a car depreciates 20% every year. If after two years the price of a car is Rs , find its original price. ANSWERS: (1) 65% (2) 15%, l, 1.56 l (3) Rs 45000, Rs (4) 200, 80 (5) 14, 21 (6) Rs (7) 1% (8) 25% (9) 50/3% (10) 10000, (11) 40000, 10000, 8000, 17.24% (12) 13.04% (13) 100/11% (14) Dec by 4% (15) 300/13% (16) 68% (17) Page 1 of 6

2 SET : 2 1. A man loses 20% of his money. After spending 25% of the remainder, he has Rs 480 left. How much money did he originally have? (Rs 800) 2. In an election, there are only two candidates. The winner polled 55% votes and won by a margin of 8756 votes. Find the total number of votes polled? (87560) 3. An alloy contains 36% zinc, 40% copper and the rest is nickel. Find in grams the quantity of each of the contents in a sample of 1 kg alloy. (360 g, 400 g, 240 g) 4. A man bought 200 eggs for Rs eggs were broken. For how much an egg should he sell so as to gain 8% in the whole transaction? (Rs 4.80 ) 5. X s weight is 25% that of Y s and 40% that of Z s. What percentage of Z s weight is Y s weight? (160%) 6. The value of a machine depreciates every year by 10%. What will be its value after 2 years if its present value is Rs 50,000? (Rs 40,050) 7. The salary of an officer has been increased by 50%. By what percent the new salary must be reduced to restore the original salary? ( %) 8. Find the percent of pure gold in 22 carat gold, if 24 carat gold is hundred percent pure gold. ( %) 9. If the CP of 18 mangoes is the same as the selling price of 16 mangoes, find the gain percent. (Gain of 12.5%) 10. If the CP of 25 chairs is equal to the SP of 30 chairs, find the loss percent.( %) 11. A girl buys lemons at 4 for Rs 3 and sells them at 5 for Rs 4. How much percent loss or gain does she make? (Gain of %) 12. A man buys a plot for Rs He sells one third at a loss of 20% and two fifths at a gain of 25%. At what price must he sell the remaining land so as to make an overall profit of 10%? (Rs ) 13. A dealer professes to sell his goods at CP, but he uses a weight of 960 g for 1 kg. Find his gain percent. (25/6 %) 14. A man bought two TV Sets for Rs He sold one at a loss of 10% and other at a profit of 10%. If the SP of each TV Set is Page 2 of 6 same, determine the CP of each set. (Rs and Rs 19125) 15. If a man were to sell his cart for Rs 720, he would lose 25%. What must he sell it for to gain 25%? (Rs 1200) 16. A toy was sold at a gain of 12%. Had it been sold for Rs 33 more, the gain would have been 14%. Find the CP of the toy. (Rs 1650) 17. A man bought an article and sold it at a gain of 10%. If he had bought it at 20% less and sold it for Rs 10 more, he would have made a profit of 40%. Find the CP of the article? (Rs 500)0 CHAPTER: FACTORISATION 1. Factorise by taking common factor: (a) 3x 2 + 6xy (b) 7xy 21 x 2 y 2 (c) 3x 2 y 2 + 2x 3 y + 9xy 2 (d) x 3 y 3 + 2x 2 y 2 + x 2 y 4 (e) 46x 2 + 2xy + 10y 3 (f) ax 2 + bx 2 + ay 2 + by 2 (g) 5a (b+c) 7b (b+c) (h) 8(a+3b) 2 4(a+3b) (i) 2x(a+b) + 3y(6a+6b) 5z(3a+3b) (j) xy(x 2 y 2 +z 2 ) + yz(x 2 y 2 +z 2 ) zx (x 2 y 2 + z 2 ) (k) ab (a+b) 2 3ab (a+b) (l) x(x y) 3 + 3xy(x y) 2. Factorise by grouping the terms: (a) a 2 + 2b + ab + 2a (b) xy + 2bx + ay + 2ab (c) 2b 2 + 8ab + 4ac + bc (d) ax by + bx ay (e) axy 2 + 3x + 2a 2 y 2 + 6a (f) 6pm + 9mq + 8pn + 12qn (g) abc 2 + abd 2 + cda 2 + cdb 2 (h) a 2 px + 2a 2 qx 2apy 4aqy + pz + 2qz (i) (x 2 + 4x) 2 + 4x 2 2x 2 y + 16x 8xy (j) x 2 + (a + b + c)x + ab + bc (k) xy (z 2 + 1) + z(x 2 + y 2 ) (l) 1 + a + b + c + ab + bc + ca + abc

3 3. Factorise: (a) 4a ab + 9b 2 [(2a+3b) 2 ] (b) x x + 25 [(x+5) 2 ] (c) 9x xy + 16y 2 [(3x+4y) 2 ] (d) 16a 2 40ab + 25b 2 [(4a 5b) 2 ] (e) x 2 + 5x + 25/4 [(x = 5/2) 2 ] (f) 49x 4 168x 2 y y 4 [(7x 2 12y 2 ) 2 ] 4. Factorise: (a) [ ( )2 ] (b) a 2 2ab + b 2 a + b [(a b) (a b a)] (c) 4x xy + 9y 2 6x 9y [(2x+3y) (2x+3y 3)] (d) x 2 + y 2 + 2(xy + yz + zx) [(x+y) (x+y+2z)] 5. Factorise: (a) (b) 4 (x + 3y) 2 28 (x + 3y) + 49 (c) 9(2x+3y) (2x 3y) (2x+3y) + 4(2x+ 3y) 2 6. Factorise: (a) x 2 4y 2 (b) 4a 2 x 2 25b 2 y 2 (c) a 2 x 2 2xy y 2 (d) 4a 2 4b 2 + 4a + 1 (e) 25x xy + y 2 z 2 (f) x 2 4y 2 + 4y 1 (g) x (1/x 2 ) y 2 (h) x 2 + (4/x 2 ) 7. Factorise: (a) 81 16x 2 (b) 5 20x 2 (c) 81x 4 y 4 (d) 2x 4 32 (e) 16x 4 1 (f) 81x y 12 (g) x 8 1 (h) 6561a 8 256b 8 8. Factorise: (a) x 2 + y 2 z 2 2xy (b) 1 + 2ab (a 2 + b 2 ) (c) 4x 2 24ab 9a 2 16b 2 (d) x 2 z 2 + y 2 p 2 + 2pz 2xy (e) a 2 b 2 c 2 2bc a b c (f) a 2 b 2 c 2 + d 2 2 (ad bc) (g) (ac + bd) 2 (ad + bc) 2 (h) x 2 y 2 z 2 + 2yz + x + y z 9. Factorise: (a) a 4 + 3a (b) a (c) x 4 + x 2 y 2 + y 4 (d) ANSWERS Q No. 5 (a) [ ] (b) [(2x+6y 7) 2 ] (c) (10x 3y) 2 (d) (2a + 3b + c) 2 Q No.9 (a) (a 2 + a + 2) (a 2 a + 2) (b) (a 2 + 2a + 2) (a 2 2a + 2) (c) (x 2 + y 2 + xy) (x 2 + y 2 xy) (d) Q. No. 6 Q. No. 7 (a) (x+2y) (x 2y) (a) (9 + 4x) (9 4x) (b) (2ax + 5by) (2ax 5by) (b) 5 (1 + 2x) (1 2x) (c) (a + x + y) (a x y) (c) (9x 2 + y 2 ) (3x + y) (3x (d) (2a + 2b + 1) (2a 2b + y) 1) (d) 2 (x 2 + 4) (x + 2) (x 2) (e) (5x + y + z) (5x + y z) (e) (4x 2 + 1) (2x + 1) (2x (f) (x + 2y 1) (x 2y + 1) 1) (g) [x (1/x) + y] [x (1/x) (f) (9x y 6 ) (3x 3 + 4y 3 ) y] (3x 3 4y 3 ) (h) [x + (2/x) + 2] [x + (2/x) (g) (x 4 + 1) (x 2 + 1) (x + 1) (x 2] 1) (h) (81a b 4 ) (9a 2 + 4b 2 ) (3a + 2b) (3a 2b) Q. No. 8. (a) (x y + z) (x y z) (b) (1 + a b) (1 a + b) (c) (2x + 3a + 4b) (2x 3a 4b) (d) (x y + p z) (x y p + z) (e) (a + b + c) (a b c 1) (f) (a d + b c) (a d b + c) (g) (ac + bd + ad + bc) (ac + bd ad bc) (h) (x + y z) (x y + z + 1) FACTORISATION BY SPLITTING THE MIDDLE TERM OF A QUADRATIC POLYNOMIAL: EXERCISE: Factorise: (a) x 2 21x + 90 Page 3 of 6

4 (b) x 2 27x (c) x 2 + 5x 84 (d) x x 150 (e) x 2 24x 180 (f) x 2 20x Factorise: (a) x x + 6 (b) x x + 12 (c) x x + 30 (d) x x Factorise: (a) a 4 + 4a (b) x x (c) x 8 x (d) y 16 63y Factorise: (a) (b) (2b 3) 2 (2b 3) 12 (c) (p + q) 2 20(p + q) 125 (d) (m + 2n) (m + n) Factorise: (a) 6x 2 + 7x + 2 (b) 9x x + 8 (c) 5x x + 3 (d) 2x x Factorise: (a) 2x 2 + 9x (b) 3x x (c) 6 3x 2 47x (d) 5 5x x (e) 2x 2 + 3x + 2 (f) 7x x Factorise: (a) ½ x 2 + 4x + 6 (b) 2x 2 x + (1/8) (c) 2x 2 (5/6)x + (1/12) (d) x 2 + (12/35)x + (1/35) (e) 21x 2 2x + (1/21) ANSWERS TO EXERCISE: 2.2 Page 4 of 6 Q.No. 1 Q. No. 2 (a) (x 6) (x 15) (a) (x + 2) (x + 3 2) (b) (x 16) (x 11) (b) (x+ 3) (x+4 3) (c) (x+12) (x 7) (c) (x+2 5) (x+3 5) (d) (x+25) (x 6) (d) (x+2 6) (x+4 6) (e) (x 30) (x+6) (f) (x 30) (x+10) Q. No. 3 Q. No. 4 (a) (a 2 + 1) (a 2 + 3) (a) [5x (1/x)+3] (b) (x 2 +32) (x+2) (x 2) [5x (1/x)+2] (c) (x 4 12) (x 4 +11) (b) (2b 7) (2b) (d) (y 8 +1) (y 4 +8) (y 4 8) (c) (p+q+5) (p+q 25) (d) (m+2n+100) (m+2n+1) Q. No. 5 Q. No. 6 (a) (2x+1) (3x+2) (b) (3x+4) (3x+2) (c) (x+3) (5x+1) (d) (x+7) (2x 3) Q. No. 7 (a) (x+6) [(x/2)+1] (b) (4x 1) [(x/2) (1/8)] (c) (6x 1) [(x/3) (1/12)] (d) [x+(1/7)] [x+(1/5)] (e) (21 x) [x (1/21)] (a) (x 2+1) (x+4 2) (b) (x 3+4) (x+2 3) (c) (3 3x 1) (2x 5 3) (d) ( 5x+1) (5x+3 5) (e) (x+ 2) ( 2x+1) (f) ( 7x+ 2) ( 7x+ 2) EXERCISE: Find the product: (a) (a 1) (a+1) (a 2 +1) (a 4 +1) [a 8 1] (b) (2x+5y) (2x 5y) [4x 2 25y 2 ] (c) (a+b+c) (a+b c) [a 2 +2ab+b 2 c 2 ] (d) (x y) (x+y) (x 2 +y 2 ) (x 4 +y 4 ) [x 8 y 8 ] 2. If x + y = 5 and xy = 6, find x 2 + y 2. (13) 3. If 2x 3y = 5 and xy = 4, find 4x 2 + 9y 2. (73) 4. If x + (1/x) = 3 find x 2 + (1/x 2 ). (7) 5. If x (1/x) = 7 find, x 2 + (1/x 2 ) and x + (1/x). (51, 53) 6. If 9x 2 + y 2 = 10 and xy = 1 then find the value of 3x + y. (2) 7. Without multiplying directly and using identity find: (a) 103 X 107 (b) 95 X 96 (c) 104 X 96 (d) 97 X 105 (e) 195 X X 105 (f) (104) 2 (g) (0.98) 2

5 CHAPTER: LINEAR EQUATION IN ONE VARIABLE SET: 1 1. Radha takes some flowers in a basket and visits three temples one by one. At each temple, she offers one half of the flowers from the basket. If she is left with 3 flowers at the end, find the number of flowers she had in the beginning. 2. The volume of water in a tank is twice that in the other. If we draw out 25 litres from the first and add it to the other, the volumes of the water in each tank will be the same. Find the volume of water in each tank. 3. X and Y are friends. They have equal amount of money in their pockets. X gave 1/3 of her money to Y as her birthday gift. Then Y gave a party at a restaurant and cleared the bill by paying half of the total money with her. If the remaining money in Y s pocket is Rs 1600, find the sum gifted by X. 4. A had 60 flowers. He offered some flowers in a temple and found that the ratio of the number of remaining flowers to that of flowers in the beginning is 3: 5. Find the number of flowers offered by A in the temple. 5. The sum of three consecutive even natural numbers is 48. Find the greatest of these numbers. 6. The sum of three consecutive odd natural numbers is 69. Find the prime number out of these numbers. 7. The sum of three consecutive numbers is 156. Find the number which is a multiple of 13 out of these numbers. 8. Find a number whose fifth part increased by 30 is equal to its fourth part decreased by Divide 54 into two parts such that one part is 2/7 of the other. 10. After 12 years, X shall be 3 times as old as he was 4 years ago. Find his present age. 11. Find the side of a square whose area is equal to the area of a rectangle with sides 6.4 m and 2.5 m. 12. Rahul walks 12 m north from his house and turns west to walk 35 m to reach his friend s house. While returning, he walks diagonally from his friend s house to reach back to his house. What distance did he walk while returning? 13. Find three numbers in the ratio 2: 3 : 5, the sum of whose squares is The perimeters of two squares are 40 and 96 m respectively. Find the perimeter of another square equal in area to the sum of the first two squares. 15. The sum of four consecutive integers is 266. What are the integers? 16. The perimeter of a rectangle is 240 cm. If its length is increased by 10% and its breadth is decreased by 20%, we get the same perimeter. Find the length and breadth of the rectangle. 17. The age of A is five years more than that of B. 5 years ago, the ratio of their ages was 3 : 2. Find their present ages. 18. If numerator is 2 less than denominator of a rational number and when 1 is subtracted from numerator and denominator both, the rational number in its simplest form is ½. What is the rational number? 19. In a two digit number, digit in units place is twice the digit in tens place. If 27 is added to it, digits are reversed. Find the number. 20. A man was engaged as typist for the month of February in He was paid Rs 500 per day but Rs 100 per day were deducted for the days he remained absent. He received Rs 9100 as salary for the month. For how many days did he work? 21. A steamer goes downstream and covers the distance between two ports in 3 h. It covers the same distance in 5 h when it goes upstream. If the stream flows at 3 km/h, then find what is the speed of the steamer upstream? 22. There are 40 passengers in a bus, some with Rs 3 tickets and remaining with Rs 10 tickets. The total Page 5 of 6

6 collection from these passengers is Rs 295. Find how many passengers have tickets worth Rs 3? 23. An employee works in a company on a contract of 30 days on the condition that he will receive Rs 120 for each day he works and he will be fined Rs 10 for each day he is absent. If he receives Rs 2300 in all, for how many days did he remain absent? 24. Kusum buys some chocolates at the rat of Rs 10 per chocolate. She also buys an equal number of candies at the rate of Rs 5 per candy. She makes a 20% profit on chocolates and 8% profit on candies. At the end of the day, all chocolates and candies are sold out and her profit is Rs 240. Find the number of chocolates purchased. 25. Distance between two places A and B is 210 km. Two cars start simultaneously from A and B in opposite direction and distance between them after 3 h is 54 km. If speed of one car is less than that of the other by 8 km/h, find the speed of each. 26. A carpenter charged Rs 2500 for making abed. The cost of materials used is Rs 1100 and the labour charges are Rs 200/hour. For how many hours did the carpenter work? 27. On dividing Rs 200 between A and B such that twice of A s share is less than 3 times B s share by 200, B s share is? 28. X thought a number, doubled it and added 20 to it. On dividing the resulting number by 25, she gets 4. Find number. 29. A three digit perfect square is such that if it is viewed upside down, the number seen is also a perfect square. What is the number? and 31 is a strange pair of numbers such that their squares 169 and 961 are also mirror images of each other. Can you find two other such pairs? 31. Mobile number of A is 9xyzp1q2r3, where (6y- 7)/(3y+9) = 1/3, (z 2 9)/(5+z 2 ) = -5/9, p + (3p/10) = 13/10, 4(q+4) = 5(q+2) and 3(r+10) = 236 and 2x + 4 = 20. Find A s mobile number. 32. Determine the missing value: = 8 = 10 =? 33. Solve: (x/2) + (x/4) + (x/5) = x 34. The present age of father is four times the age of his son. After 10 years, age of father will become three times the age of his son. Find their present ages. 35. A steamer goes downstream from one point to another in 7 h. It covers the same distance upstream in 8 h. If the speed of stream be 2 km/h, find the speed of the steamer in still water and the distance between the ports. 36. Distance between two stations A and B is 690 km. Two cars start simultaneously from A and B towards each other, and the distance between them after 6 h is 30 km. If the speed of one car is less than the other by 10 km/h, find the speed of each car. 37. Solve: Solve: Solve: 40. Solve: Solve: Solve: Solve: 44. Solve: 45. Solve: 0.16(5x 2) = 0.4x + 7 Page 6 of 6

The City School PAF Chapter Prep Section. Mathematics. Class 8. First Term. Workbook for Intervention Classes

The City School PAF Chapter Prep Section Mathematics Class 8 First Term Workbook for Intervention Classes REVISION WORKSHEETS MATH CLASS 8 SIMULTANEOUS LINEAR EQUATIONS Q#1. 1000 tickets were sold. Adult