The difference between two numbers is 48 and the difference between the arithmetic mean and the geometric mean is two more than half of 1/3 of 96.Find the numbers.

(a)49,1 (b)12,60 (c)36,84 (d)none of these

• let two no be a and b
  airthemetic mean= a+b/2
  geometric mean = sqrt(ab)
  
  by question, a-b=48-----------------------------1
  (a+b)/2 - sqrt(ab)= 18
  
  ==> a+b - 2sqrt(ab)=36
  ==> a+b= 36+ 2sqrt(ab)------------------------2
  
  by equation 1 and 2
  2a = 84+ 2sqrt(ab)
  
  so, a-sqrt(ab) =42
  
  now check the option,
  option a is satisfied the equation .........49-sqrt(49*1)= 42
  
  so ans will be 49,1
• 9 years agoHelpfull: Yes(17) No(0)
• according to the question
  airthmetic mean-geometric mean=2+1/2*1/3*96
  (49+1)/2-sqrt(49*1)=2+16
  18=18
  so a is the ans 49,1
• 8 years agoHelpfull: Yes(4) No(0)
• ans: 49,1
  description: x-y=48
  arithmetic mean - geometric mean =2 more than the half of 1/3 of 96
  => (x+y)/2 - sqrt(xy) = 2 * (1/2) *(1/3)*96
  (49+1)/2 - sqrt(49) = 18
  18 = 18
• 8 years agoHelpfull: Yes(0) No(2)
• ans: (A) 49,1
  Solution: Jst go through the options ;)
  
• 8 years agoHelpfull: Yes(0) No(0)