### Algebra Class 8th Mathematics Term 2 Tamilnadu Board Solution

##### Question 1.Solve the following equations:3x + 5 = 23Answer:Subtracting 5 from both sides,⇒ 3x + 5 – 5 = 23 – 5⇒ 3x = 18Dividing both sides by 3, ⇒ x = 6Question 2.Solve the following equations:17 = 10 - yAnswer:Subtracting 10 from both sides,⇒ 17 - 10 = 10 – y – 10⇒ 7 = -yDividing both sides by -1, ⇒ y = -7Question 3.Solve the following equations:2y - 7 = 1Answer:Adding 7 to both sides,⇒ 2y – 7 + 7 = 1 + 7⇒ 2y = 8Dividing both sides by 2, ⇒ y = 4Question 4.Solve the following equations:6x = 72Answer:Dividing both sides by 6, ⇒ x = 12Question 5.Solve the following equations: Answer:Multiplying both sides by 11, ⇒ y = -77Question 6.Solve the following equations:3(3x - 7) = 5(2x - 3)Answer:9x – 21 = 10x – 15⇒ 10x – 15 – 9x + 21 = 0⇒ x + 6 = 0⇒ x = -6Question 7.Solve the following equations:4(2x - 3) + 5(3x - 4) = 14Answer:⇒ 8x – 12 + 15x – 20 = 14⇒ 8x + 15x = 14 + 12 + 20⇒ 23x = 46Dividing both sides by 23, ⇒ x = 2Question 8.Solve the following equations: Answer:⇒ 7(x – 7) = 5(x – 5)⇒ 7x – 49 = 5x – 25⇒ 7x – 5x = 49 – 25⇒ 2x = 24Dividing both sides by 2, ⇒ x = 12Question 9.Solve the following equations: Answer:⇒ 5(2x + 3) = 3(3x + 7)⇒ 10x + 15 = 9x + 21⇒ 10x – 9x = 21 – 15⇒ x = 6Question 10.Solve the following equations: Answer:  ⇒ 7m × 2 = 12⇒ 14m = 12Dividing both sides by 2,  Question 11.Frame and solve the equations for the following statements:Half of a certain number added to its one third gives 15. Find the number.Answer:Let the number be xThen according to question,     ⇒ x = 18Hence, the number is 18.Question 12.Frame and solve the equations for the following statements:Sum of three consecutive numbers is 90. Find the numbers.Answer:Let the numbers be x, x+1 and x+2Then according to the question,x + (x + 1) + (x + 2) = 90⇒ x + x + 1 + x + 2 = 90⇒ 3x + 3 = 90⇒ 3x = 90 – 3⇒ 3x = 87 ⇒ x = 29⇒ x + 1 = 29 + 1 = 30⇒ x + 2 = 29 + 2 = 31Hence, the numbers are 29, 30 and 31.Question 13.Frame and solve the equations for the following statements:The breadth of a rectangle is 8 cm less than its length. If the perimeter is 60 cm, find its length and breadth.Answer:Let breadth of rectangle = xThen length of rectangle = x + 8Perimeter = 60 cmWe know that,Perimeter of rectangle = 2 (length of rectangle + breadth of rectangle)⇒ 60 = 2(x + (x + 8))⇒ 60 = 2(x + x + 8)⇒ 60 = 2(2x + 8)⇒ 60 = 4x + 16⇒ 4x = 60 – 16⇒ 4x = 44⇒ x = 11⇒ x + 8 = 11 + 8 = 19Hence, breadth of rectangle = 11 cmlength of rectangle = 19 cmQuestion 14.Frame and solve the equations for the following statements:Sum of two numbers is 60. The bigger number is 4 times the smaller one. Find the numbers.Answer:Let the smaller number be xThen bigger number = 4xThen according to the question,x + 4x = 60⇒ 5x = 60 ⇒ x = 12⇒ 4x = 4 × 12 = 48Hence, the numbers are 12 and 48.Question 15.Frame and solve the equations for the following statements:The sum of the two numbers is 21 and their difference is 3. Find the numbers. (Hint: Let the bigger number be x and smaller number be x – 3)Answer:Let the bigger number be xThen the smaller number = x – 3 [∵ the difference is 3]Then according to the question,x + (x – 3) = 21⇒ 2x – 3 = 21⇒ 2x = 21 + 3 ⇒ x = 12⇒ x – 3 = 12 – 3 = 9Hence, the numbers are 12 and 9.Question 16.Frame and solve the equations for the following statements:Two numbers are in the ratio 5 : 3. If they differ by 18, what are the numbers?Answer:Let the numbers be 5x and 3xThen according to the question,5x – 3x = 18⇒ 2x = 18 ⇒ x = 9⇒ 5x = 5 × 9 = 45⇒ 3x = 3 × 9 = 27Hence, the numbers are 45 and 27.Question 17.Frame and solve the equations for the following statements:A number decreased by 5% of it is 3800. What is the number?Answer:Let the number be xThen according to the question,     ⇒ x = 4000Hence, the number is 4000.Question 18.Frame and solve the equations for the following statements:The denominator of a fraction is 2 more than its numerator. If one is added to both the numerator and their denominator the fraction becomes Find the fraction.Answer:Let the numerator be xThen the denominator = x + 2Then according to the question,  ⇒ 3(x + 1) = 2(x + 3)⇒ 3x + 3 = 2x + 6⇒ 3x – 2x = 6 – 3⇒ x = 3 (Numerator)⇒ x + 2 = 3 + 2 = 5 (Denominator)Hence, the fraction is Question 19.Frame and solve the equations for the following statements:Mary is 3 times older than Nandhini. After 10 years the sum of their ages will be 80. Find their present ages.Answer:At present,Let age of Nandini = xThen age of Mary = 3xAfter 10 years,Age of Nandini = x + 10Age of Mary = 3x + 10Then according to the question,[x + 10] + [3x + 10] = 80⇒ x + 10 + 3x + 10 = 80⇒ 4x + 20 = 80⇒ 4x = 80 – 20⇒ 4x = 60⇒ x = 15⇒ 3x = 3 × 15 = 45Hence, Present age of Nandini = 15 yearsPresent age of Mary = 45 yearsQuestion 20.Frame and solve the equations for the following statements:Murali gives half of his savings to his wife, two third of the remainder to his son and the remaining ` 50,000 to his daughter. Find the shares of his wife and son.Answer:Let the savings of Murali be x          According to the question, ⇒ x = 50000 × 6⇒ x = 300000  Hence, Share of his wife = Rs 1,50,000Share of his son = Rs 1,00,000

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