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      Question

      I.8(x+3) +  8(-x) =72 

      II. 5(y + 5) + 5(-y) = 150  In the following questions, two equations numbered I and II are given. You have to solve both the equations and find out the correct option.  Give answer 
      A If x ≥ y Correct Answer Incorrect Answer
      B If x ≤ y Correct Answer Incorrect Answer
      C If x > y Correct Answer Incorrect Answer
      D If x < y Correct Answer Incorrect Answer
      E If x = y or relationship between x and y cannot be established Correct Answer Incorrect Answer

      Solution

      I. 8(x+3) +  8(-x) =72  8x × 83 +  (1/8)x - 72 = 0  Let 8x = a 512a +  1/a - 72 = 0  512a² + a - 72a = 0  512a² - 72a + 1 = 0  512a² - 64a - 8a + 1 = 0  64a (8a-1) -1(8a-1) = 0  (64a-1) (8a-1) = 0  a =  1/8, 1/64  8x = 1/8  x = -1   8x = 1/64  x = -2   II. 5(y + 5) + 5(-y) = 150 55 × 5y + (1/5)y - 150 = 0  Let 5y = b 3125b + 1/b - 150 = 0  3125b² - 150b + 1 = 0  3125b² - 125b - 25b + 1 = 0  125b(25b-1) -1(25b-1) = 0  b = 25, 125  5y = 1/25  y = -2  5y = 1/125  y = -3  Hence, x ≥ y 

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