NCERT Solutions For Class 8 Subject-wise

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NCERT Solutions for Class 8 Subject-wise Class 8 Maths Class 8 Science – Physics Class 8 Science – Biology Class 8 Science – Chemistry Class 8 Social Science – History Class 8 Geography Class 8 General Knowledge Class 8 Civics

ons/print/?show answer 1&show topic 1&show solution 1&page 1&qid 463560%2C 4635 #463518Topic: Solving Linear Equations in One VariableSolve the equation:x 2 7SolutionTransporting 2 to RHS, we obtainx 7 2x 9#463519Topic: Solving Linear Equations in One VariableSolve the equation:y 3 10SolutionTransporting 3 to RHS, we obtainy 10 3 7 y 7#463520Topic: Solving Linear Equations in One VariableSolve the equation:6 z 2SolutionTransporting 2 to LHS, we obtain6 2 zz 4#463522Topic: Solving Linear Equations in One VariableSolve the equation:317 x 77SolutionTransportingx 17714x 7 3to RHS, we will get,737x 2#463524Topic: Solving Linear Equations in One VariableSolve the equation:6x tions/print/?show answer 1&show topic 1&show solution 1&page 1&qid 463560%2C 463564%2C 46 1/28

ons/print/?show answer 1&show topic 1&show solution 1&page 1&qid 463560%2C 4635 Given, 6x 12Divide both sides by 6,We will get6x 12 66x 2#463525Topic: Solving Linear Equations in One VariableSolve the equation:t 105Solutiont 105Multiply both sides by 5, we will get,t5 5 10 5t 50#463527Topic: Solving Linear Equations in One VariableSolve the equation:2x3 18Solution2x3 18Multiply both sides by2x3 32 18 32, we will get32x 27#463528Topic: Solving Linear Equations in One VariableSolve the equation:1.6 y1.5Solution1.6 y1.5Multiply both sides by 1.5, we will get1.6 1.5 y1.5 1.5y 2.4#463529Topic: Solving Linear Equations in One VariableSolve the equation:7x 9 tions/print/?show answer 1&show topic 1&show solution 1&page 1&qid 463560%2C 463564%2C 46 2/28

ons/print/?show answer 1&show topic 1&show solution 1&page 1&qid 463560%2C 4635 Transport 9 to RHS, we will get7x 9 167x 25Now, divide both sides by 7, we will get7x 25 7725x 7#463530Topic: Solving Linear Equations in One VariableSolve the equation:14y 8 13SolutionTransport 8 to RHS14y 13 814y 21Divide both sides by 14, we will get,14y14y 211432#463532Topic: Solving Linear Equations in One VariableSolve the equation:17 6p 9SolutionGiven, 17 6p 9Transport 17 to RHS, 6p 9 176p 8Divide both sides by 6We will get,P 6p6 86 43#463533Topic: Solving Linear Equations in One VariableSolve the equation:x7 1 stions/print/?show answer 1&show topic 1&show solution 1&page 1&qid 463560%2C 463564%2C 46 3/28

ons/print/?show answer 1&show topic 1&show solution 1&page 1&qid 463560%2C 4635 Transport 1 to RHSx37 15x3x3 17 15 15 8 15Multiply both sides by 3, we will get,x 815 x 3 85#463536Topic: Solving Linear Equations in One VariableIf you subtract12from a number and multiply the result by12, you get18. What is the number?SolutionLet the number : xAs per the question's1112 2 8( )x Multiply both sides by 2,x 121 x x x 414, transport 12to RHS122 1434#463538Topic: Solving Linear Equations in One VariableThe perimeter of a rectangular swimming pool is 154 m. Its length is 2 m more than twice its breadth. What are the length and the breadth of the uestions/print/?show answer 1&show topic 1&show solution 1&page 1&qid 463560%2C 463564%2C 46 4/28

ons/print/?show answer 1&show topic 1&show solution 1&page 1&qid 463560%2C 4635 Let the breadth be b mThe length will be (2b 2)mPerimeter of swimming pool 2(l b) 154 m2(2b 2 b) 1542(3b 2) 154Dividing both sides by 2, we will get,3b 2 77Transport 2 to RHS2b 75Divide both sides by 3b 25 ml 2b 2 2 25 2 52 m#463540Topic: Solving Linear Equations in One VariableThe base of an isosceles triangle is43cm. The perimeter of the triangle is6215cm. What is the length of either of remaining equal sides?SolutionLet the length of equal sides by x cm.Perimeter x x third side2x 4362 15Transport4362 42x 15 3 x to RHS62 2015 2x 4215Divide sides by 2, x x 421575#463541Topic: Solving Linear Equations in One VariableSum of two numbers is 95. If one exceeds the other number 15, ﬁnd the /questions/print/?show answer 1&show topic 1&show solution 1&page 1&qid 463560%2C 463564%2C 46 5/28

ons/print/?show answer 1&show topic 1&show solution 1&page 1&qid 463560%2C 4635 Let one number x, The other will be: x 15As per the question:x x 15 95, 2x 80x 40One number 40Other number will be: x 15 40 15 55#463543Topic: Solving Linear Equations in One VariableTwo numbers are in the ratio 5 : 3. If they diﬀer by 18, what are the numbers?SolutionLet x be common ratio numbers will be 5x and 3x respectively.Diﬀerence between these numbers 185x 3x 182x 18Divide both sides by 2.2x2 182x 9 First number 5x 5 9 45Second number 3x 3 9 27#463545Topic: Solving Linear Equations in One VariableThree consecutive integers add up to 51. What are these integersSolutionLet 3 consecutive integers be x, x 1, x 2Sum of 3 numbers x x 1 x 2 3x 33x 3 51,Transport 3 to RHS3x 48Divide both sides by 33x 48 33 x 16 x 16 1 17 x 16 2 18Integers are 16, 17, 18#463547Topic: Solving Linear Equations in One VariableThe sum of 3 consecutive multiples of 8 is 888. Find the nt/questions/print/?show answer 1&show topic 1&show solution 1&page 1&qid 463560%2C 463564%2C 46 6/28

ons/print/?show answer 1&show topic 1&show solution 1&page 1&qid 463560%2C 4635 Let 3 consecutive multiple of 88x, 8(x 1), 8(x 2)Sum 8x 8(x 1) 8(x 2) 8888(x x x 1 2) 8883(x 1) 111x 1 1113x 1 37x 36First multiple 8x 8 36 288Second 8(x 1) 8 37 296Third 8(x 2) 8 38 304#463549Topic: Solving Linear Equations in One VariableThree consecutive integers are such that when they are taken in increasing order and multiplied by 2, 3 and 4 respectively, they add upto 74. Find these numbers.SolutionLet 3 consecutive integers: x, x 1, x 2As per the question: 2x 3(x 1) 4(x 2) 749x 11 74Transpose 11 to RHS9x 63Divide both sides by 9x 639,x 7x 7,x 1 7 1 8x 2 7 2 9Numbers are 7, 8 and 9#463554Topic: Solving Linear Equations in One VariableThe ages of Rahul and Haroon are in ratio 5 : 7. Four years later the sum of their ages will be 56 years. What are their present age?SolutionLet Rahul's and Haroon's age's common ration be x. Age of Rahul and Haroon will be 5x and 7x yearsAfter, 4 years, Age of Rahul and Haroon will be (5x 4) and (7x 4) years respectively.Now, As per the questionAfter 4 years, Sum of age of Rahul and Haroon is 56 yrs (5x 4 7x 4) 5612x 8 56Transpose 8 to RHS12x 48Divide both sides by 12, x 4Rahul's age 5x 5 4 20 yearsHaroon's age 7x 7 4 28 /print/?show answer 1&show topic 1&show solution 1&page 1&qid 463560%2C 463564%2C 46 7/28

ons/print/?show answer 1&show topic 1&show solution 1&page 1&qid 463560%2C 4635 #463558Topic: Solving Linear Equations in One VariableThe number of boys and girls in a class are in ratio 7 : 5. The number of boys is 8 more than the number of girls. What is the total class strength?SolutionLet the common ratio between number of boys and girls be xNumber of boys 7xNumber of girls 5xAs per the question,Number of boys Number of girls 87 x 5x 8Transpose 5x to LHS, we will get7 x 5x 82x 8Divide both sides by 2x 4No. of boys 7x 7 4 28No. of girls 5x 5 4 20Total class students 28 20 48#463560Topic: Solving Linear Equations in One VariableBaichung's father is 26 years younger than Baichung's grandfather and 29 years older than Baichung. The sum of the ages of all the three is 135 years. What is the age of eachof each one of them?SolutionLet age of Baichung's father age be x years Baichung's age and his grandfather's age (x 29) and (x 26) yrs respectively.As per the question, Sum of ages of 3 people 135 years x x 29 x 26 1353x 3 135Transpose 3 to RHS, we will get,3x 138Divides both sides by 3, we will getx 1383 x 46Baichung's father age x 46 yearsBaichung's age x 29 46 29 17 yearsBaichung's grandfather's age x 26 46 26 72 years#463564Topic: Solving Linear Equations in One VariableFifteen years from now Ravi's age will be four times his present age. What is Ravi's present estions/print/?show answer 1&show topic 1&show solution 1&page 1&qid 463560%2C 463564%2C 46 8/28

ons/print/?show answer 1&show topic 1&show solution 1&page 1&qid 463560%2C 4635 Let Ravi's present age : xFifteen years later, Ravi's age 4 xx 15 4x15 4x x3x 15 x 5Ravi's present age 5 years#463565Topic: Solving Linear Equations in One VariableA rational number's such that when you multiply it by52and add23to the product, you get 712. What is the number?SolutionLet the number be x52x 23 7 12Transpose5x2 52 712x x 232to RHS3 151212Rational number 12#463568Topic: Solving Linear Equations in One VariableLakshmi is a cashier in a bank. She has currency notes of denominations Rs. 100, Rs. 50 and Rs. 10 respectively. The ratio of number of these notes is 2 : 3 : 5. The total cash withlakshmi is Rs. 4, 00, 000. How many notes of each denomination does she have?SolutionLet the number of notes of diﬀerent denomination be x. Numbers of Rs100 notes, 50 notes and Rs10 notes will be 2x, 3x and 5x respectively.Amount of 100 Rs notes Rs100 2x 200xAmount of 50 Rs notes Rs50 3x 150xAmount of 10 Rs notes Rs10 5x 50xAs per the questionTotal amount 400000200x 150x 50x 400000400x 400000, x 1000No of Rs 100 notes 2x 2 1000 2000No of Rs 50 notes 3x 3 1000 3000No of Rs 10 notes 5x 5 1000 5000#463570Topic: Solving Linear Equations in One ons/print/?show answer 1&show topic 1&show solution 1&page 1&qid 463560%2C 463564%2C 46 9/28

ons/print/?show answer 1&show topic 1&show solution 1&page 1&qid 463560%2C 4635 I have a total of Rs 300 in coins of denomination Re1, Rs2 and Rs5. The number of Rs2 coins is 3 times the number of Rs5 coins. The total number of coins is 160. How manycoins of each denomination are with meSolutionLet number of Rs5 coins be xNumber of Rs 2 coins 3 Number of 5 Rs coins 3xNumber of Re1 coins 160 (x 3x) 160 4xAmount of Rs5 coins 5 x 5xAmount of Rs2 coins 2 3x Rs6xAmount of Re1 coins (160 4 x) 160 4xAs per the question, Total amount Rs300160 4x 5x 6x 3007x 300 160x 1407x 20Number of Re 1 coins 160 4x 160 4 20 80Number of Rs2 coins 3x 3 20 60Number of Rs5 coins x 20#463572Topic: Solving Linear Equations in One VariableThe organisers of an essay competition decide that winner is the competition gets a prize of Rs 100 and a participation who does not win gets a prize of Rs25. The total prizemoney distributed is Rs3000. Find number of winners, if total number of participants is 63.SolutionLet the number of winners : x Then number of non winners or those who aid not win 63 xThe money given to winners Rs100x and money given to participants who didn't win Rs25(63 x)As per the question:100x 1575 25x 3000Transpose 1575 to RHS75x 1425Now divide both sides by 75,We will get x 142575 x 19#463591Topic: Solving Linear Equations in One ons/print/?show answer 1&show topic 1&show solution 1&page 1&qid 463560%2C 463564%2C 4 10/28

ons/print/?show answer 1&show topic 1&show solution 1&page 1&qid 463560%2C 4635 Solve the following equation and check your results:3x 2x 18SolutionTranspose 2x to LHS,3x 2x 18x 18LHS 3x 3 18 54RHS 2x 18 2 18 18 36 18 54LHS RHS#463592Topic: Solving Linear Equations in One VariableSolve the following equation and check your results:5t 3 3 t 5SolutionTranspose 3 to RHS and 3t to LHS5t 3 t 3 52t 2On dividing both sides by 2, we gett 1LHS 5t 3 5 ( 1) 3 5 3 8RHS 3t 5 3 ( 1) 5 3 5 8LHS RHSHence proved#463602Topic: Solving Linear Equations in One VariableSolve the following equation and check your results:5x 9 5 3 xSolutionTranspose 3x to LHS and 9 to RHS5x 3 x 5 92x 4x 2LHS 5x 9 5( 2) 9 10 9 1RHS 5 3x 5 3( 2) 5 6 1LHS RHSHence proved#463604Topic: Solving Linear Equations in One VariableSolve the following equation and check your results:4z 3 6 2 ions/print/?show answer 1&show topic 1&show solution 1&page 1&qid 463560%2C 463564%2C 4 11/28

ons/print/?show answer 1&show topic 1&show solution 1&page 1&qid 463560%2C 4635 Transpose 2z to LHS and 3 to RHS4z 2 z 6 32z 3z 32LHS 4z 3 4 32 3 9RHS 6 2z 6 2 32 6 3 9LHS RHSHence proved#463606Topic: Linear Equations in One VariableThe taxi fare in a city is as follows: For the ﬁrst kilometre, the fare is 8 and for the subsequent distance it is 5 per km. Taking the distance covered as x km and total fare as Rs.y,write a linear equation for this information and draw its questions/print/?show answer 1&show topic 1&show solution 1&page 1&qid 463560%2C 463564%2C 4 12/28

ons/print/?show answer 1&show topic 1&show solution 1&page 1&qid 463560%2C 4635 x012y3813Taxi fare for ﬁrst kilometer Rs. 8Taxi fare for subsequent distance Rs. 5Total distance covered xTotal fare ySince the fare for ﬁrst kilometer Rs.8According to problem,Fare for (x– 1) kilometer 5(x 1)So, the total fare y 5(x 1) 8 y 5(x 1) 8 y 5x – 5 8 y 5x 3Hence, y 5x 3 is the required linear equation.Now the equation isy 5x 3.(1)Now, putting the value x 0 in (1)y 5 0 3y 0 3 3 So the solution is (0, 3)Putting the value x 1 in (1)y 5 1 3y 5 3 8. So the solution is (1, 8)Putting the value x 2 in (1)y 5 2 3y 10 3 13. So the solution is (2, 13)#463608Topic: Solving Linear Equations in One VariableSolve the following equation and check your results:2x 1 14 ions/print/?show answer 1&show topic 1&show solution 1&page 1&qid 463560%2C 463564%2C 4 13/28

ons/print/?show answer 1&show topic 1&show solution 1&page 1&qid 463560%2C 4635 Transpose 1 to RHs and x to LHS2x x 14 13x 15Divide both sides by 3We will get,x 5LHS 2x 1 2 5 1 10 1 9RHS 14 x 14 5 9LHS RHHence proved#463610Topic: Solving Linear Equations in One VariableSolve the following equation and check your results:8x 4 3(x 1) 7Solution8x 4 3(x 1) 78x 4 3 x 48x 3 x5x 0x 0LHS 8x 4 8 0 4 4RHS 3(x 1) 7 3(0 1) 7 3 7 4LHS RHSHence proved#463612Topic: Solving Linear Equations in One VariableSolve the following equation and check your results:x 45(x 10)Solutionx 4(x 10)5Multiply both sides by 5,5x 4(x 10)5x 4x 40Transpose 4x to LHS5x 4x 40x 40LHS x 40RHS 45(x 10) 45(40 10) 45 50 40LHS RHSHence proved#463613Topic: Solving Linear Equations in One ons/print/?show answer 1&show topic 1&show solution 1&page 1&qid 463560%2C 463564%2C 4 14/28

ons/print/?show answer 1&show topic 1&show solution 1&page 1&qid 463560%2C 4635 Solve the following equation and check your results:2x37x 1 315Solution7xTranspose2x33x157x to LHS and 1 to RHS15 3 1 15x 2 10x 7x 215 25Multiply both sides by 5,x 102xLHS 1 3RHS 23 10 1 2337x71414 9 23 3 10 3 3 1515333LHS RHSHence proved#463615Topic: Solving Linear Equations in One VariableSolve the following equation and check your results:2y 53 26 y3SolutionTranspose2y y 3y 3y 5326to RHS and y to LHS 35326 53213 3y 7Divide both sides by 3y 73LHS 2y RHS 2635 2 7 5 14 5 19 3333 33 y 263 73 26 73 193LHS RHSHence proved.#463619Topic: Solving Linear Equations in One ons/print/?show answer 1&show topic 1&show solution 1&page 1&qid 463560%2C 463564%2C 4 15/28

ons/print/?show answer 1&show topic 1&show solution 1&page 1&qid 463560%2C 4635 Solve the following equation and check your results:3 m 5m 85SolutionTranspose 5m to LHS,3 m 5m 2m 85 85Multiply both sides by 52m 5 84 m 5LHS 3m 3 RHS 5m 8545 125 (5 45) 85 20 85 125LHS RHSHence proved#463620Topic: Linear Equations in One VariableGive the geometric representations of 2x 9 0 as an equation(i) in one variable(ii) in two variableSolution(i) In one variableGiven equation is 2x 9 0 2x 9 x 92 4.5(ii) Given equation is 2x 9 0 2x 0 y 9 0 2x 9 x 92 4.5It is line parallel to y-axis at a negative distance.Two points lying it are the points A( 4.5, 0), B( 4.5, rint/?show answer 1&show topic 1&show solution 1&page 1&qid 463560%2C 463564%2C 4 16/28

ons/print/?show answer 1&show topic 1&show solution 1&page 1&qid 463560%2C 4635 #463621Topic: Solving Linear Equations in One VariableAmina thinks of a number and subtracts52from it. She multiplies the result by 8. The result now obtained is 3 times the same number she thought of what is the number?SolutionLet the number be xAs per the question58 x 2 3x( )8x 20 3x8x 3x 205x 20x 4Number is 4.#463622Topic: Solving Linear Equations in One VariableA positive number is 5 times another number. If 21 is added to both the numbers, then one of the new numbers becomes twice the other new number. What are the numbers?SolutionLet the numbers be x and 5x, As per the question21 5x 2(x 21)21 5x 2x 425x 2x 42 213x 21x 7 Numbers are x 7 and 5x 7 5 35#463623Topic: Solving Linear Equations in One VariableSum of the digits of a two digit number is 9. When we in interchange the digit it is found that the resulting new number is greater than the original number by 27. What is the twodigit questions/print/?show answer 1&show topic 1&show solution 1&page 1&qid 463560%2C 463564%2C 4 17/28

ons/print/?show answer 1&show topic 1&show solution 1&page 1&qid 463560%2C 4635 Let the digits at tens place and ones place: x and 9 x respectively. original number 10x (9 x) 9x 9Now Interchange the digits: Digit at ones place and tens place: x and 9 x respectively. New number: 10(9 x) x 90 10x x 90 9xAS per the questionNew number Original number 2790 9x 9x 9 2790 9x 9x 3618x 54x 5418x 3Digit at tens place 3 and one's place : 6 Two digit number: 36#463626Topic: Solving Linear Equations in One VariableOne of the two digits of a two digit number is three times the other digit. If you interchange the digit of this two digit number and add the resulting number to the originalnumber, you get 88. What is the original numberSolutionLet the digits at tens place: x and ones place: 3x original number 10x 3x 13xInterchange the digits,Digits at ones place and tens place will be x and 3xNumbers: 10 3x x 30x x 31xAs per the questionsOriginal number New number 8813x 31x 8844x 88x 2Original number 13x 13 2 26Or interchanging them, we will get 62#463631Topic: Solving Linear Equations in One VariableShobo's mother's present age is 6 times shobo's present age. Shobo's age ﬁve years from now will be one third of this mother's present age. What are their present uestions/print/?show answer 1&show topic 1&show solution 1&page 1&qid 463560%2C 463564%2C 4 18/28

ons/print/?show answer 1&show topic 1&show solution 1&page 1&qid 463560%2C 4635 Let Shobo's age be x years. His mother's age will be: 6x yearsAfter 5 years, Shobo's age shobo's mother's present age3As per the question, the equationx 5 6x3x 5 2xx 5Present age of shobo: 5 yearsShobo's mother age: 6x 6 5 30 years#463635Topic: Solving Linear Equations in One VariableThere is a narrow rectangular plot, reserved for a school, in mahuli village. The length and breadth of plot are in ratio 11 : 4. At the rate Rs100 per metre will cost the villagepanchayat Rs75, 000 to fence the plot. What are dimensions of plotSolutionLet the length and breadth's common ratio: x in metre Length : 11x and Breadth : 4xPerimeter 2(l b) 2(11x 4x) 30xAs per the question:Cost of fencing plot at rate of Rs. 100 per meter is Rs. 75000 100 Perimeter 750003000x 75000x 25Length 11 x 11 25 275 mBreadth 4x, 4 25 100 m#463636Topic: Solving Linear Equations in One VariableHasan buys 2 kinds of cloth material for school uniform, shirt material that costs him Rs. 50 per metre and trouser material that costs him 90 per metre. For every 2 metres oftrouser material he buys 3 metres of shirt material. He sells the material at 12% and 10% proﬁt respectively. His total sale is Rs. 36660. How much trouser material did he buySolutionLet 2m of trouser material and 3m of shirt material be bought by Hasan. Selling price of trouser material/ metre Rs. 90 91 12100 90 10.8 Rs. 100.80(Selling price of shirt material per metre Rs. 50 50 10100) 50 5 Rs. 55 Total amount of selling 36660100.8 2x 55 3x 36660366.60x 36660x 100Trouser material 2x 2 100m 200 nt/?show answer 1&show topic 1&show solution 1&page 1&qid 463560%2C 463564%2C 4 19/28

ons/print/?show answer 1&show topic 1&show solution 1&page 1&qid 463560%2C 4635 #463640Topic: Solving Linear Equations in One VariableHalf of a herd of deer are glazing in the ﬁled and three fourth of remaining are playing nearby. The rest 9 are drinking water from pond. Find number of deer in the herdSolutionLet number of deer be xNo. of deer grazing:x2No, of deer playing nearby 34No. of remaining deer3 x x 24( )3 4x23x 8No. of deer drinking water from pond 9x 3xx 2 8 9(x x x8()4x 3 x7x88) 9 9 9x 72Total no. of deer 72#463641Topic: Solving Linear Equations in One VariableA grandfather is 10 times older than his granddaughter. He is also 54 years older than her. Find their present agesSolutionLet grand daughter's age: x Grandfather's age: 10xAs per the questionsGrandfather's age Grand daughter's age 5410x x 549x 54x 6Grand daughter's age 6 years#463646Topic: Solving Linear Equations in One VariableAman's age is 3 times his son's age. Ten years ago he was ﬁve times his son's age. Find their present estions/print/?show answer 1&show topic 1&show solution 1&page 1&qid 463560%2C 463564%2C 4 20/28

ons/print/?show answer 1&show topic 1&show solution 1&page 1&qid 463560%2C 4635 Let Aman's son age: x Aman's age will be 3xTen years ago, their ages was (x 10) and (3x 10) respectivelyAs per the question's10 years ago, Aman's age 5 (Aman's son's age 10 yrs age)3x 10 5(x 10)3x 10 5x 502x 40x 20Aman's son's age x 20 years and Aman's age 3x 3 20 60 years#463650Topic: Solving Linear Equations in One VariableSolve linear equation:1x 5x 1 34Solution1x 5 xx3 13 120x 15to RHS, LCM 33.(i)345 452x RHS 1 4to LHS and3LHS x 3 x 1x4xTransposex 1 315, LCM 20920. (2)Equate (1) and (2)2x9 320Multiply both sides by 60We will get2x3 60 920 602x 20 9 340x 27x 2740#463652Topic: Solving Linear Equations in One ons/print/?show answer 1&show topic 1&show solution 1&page 1&qid 463560%2C 463564%2C 4 21/28

ons/print/?show answer 1&show topic 1&show solution 1&page 1&qid 463560%2C 4635 Solve linear equation:n2 3n5n 4 216SolutionLCM of 2, 4 and 6 is 126n 9n 10n 21127n12 21Multiply both sides by 127n12 12 21 127n 252n 2527n 36#463654Topic: Solving Linear Equations in One VariableSolve linear equation:x 7 8x3 176 5x2SolutionTranspose5x2to LHS and 7 to RHSWe get,x 5x2 LHS : x 8x35x2 176 78x3LCM of 2 and 6 6LHC x RHS :1765x2 7 8x3 17 4266x 15x 16x6 256 5x6. (1). (2)LHS RHS (equate (1) and (2))5x 25 66x 5#463657Topic: Solving Linear Equations in One VariableSolve linear equation:x 5 x 3 tions/print/?show answer 1&show topic 1&show solution 1&page 1&qid 463560%2C 463564%2C 4 22/28

ons/print/?show answer 1&show topic 1&show solution 1&page 1&qid 463560%2C 4635 x 5 x 3 35Multiply both sides by 15, we will getx 53x 3 15 5 155(x 5) 3(x 3)5x 25 3x 9Transpose 25 to RHS and 3x to LHSWe will get,5x 3x 25 92x 1616x 2x 8#463660Topic: Solving Linear Equations in One VariableSolve linear equation:3 t 2 2t 3 2 t433Solution3t 2 42t 33 23 t,LCM of 3 and 4 is 12Multiply both sides by 123t 22t 3212 3 t 12( ) ( ) ( )12 433(3t 2) 4(2t 3) 8 12t9t 6 8t 12 8 12tt 18 8 12tTranspose 12t to LHS and 48 to RHSt 12t 8 1813t 26t 26 213#463662Topic: Solving Linear Equations in One VariableSolve linear equation:m m 1m 2 1 23SolutionMultiply both sides by 6(6 m m 1m 2 1 3 62)()6 m 3 m 3 6 2m 43m 3 10 2mTranspose 2m to LHS and 3 to RHS5m 7m int/?show answer 1&show topic 1&show solution 1&page 1&qid 463560%2C 463564%2C 4 23/28

ons/print/?show answer 1&show topic 1&show solution 1&page 1&qid 463560%2C 4635 #463664Topic: Solving Linear Equations in One VariableSimplify and solve the following linear equation:3(t 3) 5(2t 1)Solution3t 9 10t 5Transpose 10t to LHS and 9 to RHS3t 10t 5 9 7t 14t 147t 2#463665Topic: Solving Linear Equations in One VariableSimplify and solve the following linear equation:15(y 4) 2(y 9) 5(y 6) 0Solution15y 60 2y 18 5y 30 0 18y 12 0 y y 12832#463667Topic: Solving Linear Equations in One VariableSimplify and solve the following linear equation:3(5z 7) 2(9z 11) 4(8z 13) 17Solution15z 21 18z 22 32z 52 17 3z 1 32z 69Transpose 32z to LHS and 1 to RHS 32z 3z 69 135z 70z 7035z 2#463669Topic: Solving Linear Equations in One VariableSimplify and solve the following linear equation:0.25(4f 3) 0.05(10f tions/print/?show answer 1&show topic 1&show solution 1&page 1&qid 463560%2C 463564%2C 4 24/28

uestions/print/?show answer 1&show topic 1&show solution 1&page 1&qid 463560%2C 4635 (4f 3) 5100(10f 9)5(4f 3) 10f 920f 15 10f 9Transpose 10f to LHS and 15 to RHS10f 6f 610f 0.6#463671Topic: Solving Linear Equations in One VariableSolve the following equation:8x 33x 2SolutionGiven,8x 33x 2Multiply both sides by 3x8x 3 2 3 x8x 3 6xTranspose 6x to LHS and 3 to RHS8x 6x 32x 3x 32#463675Topic: Solving Linear Equations in One VariableSolve the following equation:9x 157 6xSolutionGiven,9x 157 6xMultiply both sides by 7 6x9x 15(7 6x)9x 105 90xTranspose 90x to LHS9x 90x 10599x 105x 10599 x 3533#463678Topic: Solving Linear Equations in One VariableSolve the following equation:z4 z 15 ions/print/?show answer 1&show topic 1&show solution 1&page 1&qid 463560%2C 463564%2C 4 25/28

questions/print/?show answer 1&show topic 1&show solution 1&page 1&qid 463560%2C 4635 z4 z 15 9Multiply both sides by 9(z 15)9z 4(z 15)9z 4z 605z 60z 605z 12#463682Topic: Solving Linear Equations in One VariableSolve the following equation:3y 42 6y 25Solution3y 42 6y 25Multiply both sides by 5(2 6y)5(3y 4) 2(2 6y)15y 20 4 12yTranspose 12y to LHS and 20 to RHS15y 12y 4 203y 24y 8#463684Topic: Solving Linear Equations in One VariableSolve the following equation:7y 4 4 y 23Solution7y 4 4 y 23Multiply 3(y 2) to both sides3(7y 4) 4(y 2)21y 12 4y 821y 4y 8 1225y 20y 2025 y 45#463687Topic: Solving Linear Equations in One VariableThe ages of Hari and Harry are in ratio 5 : 7. Four years from now the ratio of there ages will be 3 : 4. Find their present agesSolutionhttps://community.toppr.com/content/

8 15 Multiply both sides by 3, we will get, x 8 15 3 x 8 5 #463536 Topic: Solving Linear Equations in One Variable If you subtract 1 2 from a number and multiply the result by 1 2, you get 1 8. What is the number? Solution Let the number : x As per the question's x 1 2 1 2 1