The sum of two numbers is 15 and their geometric mean is 20% lower than their arithmetic mean.Find the numbers.

(a)11,4 (b)12,3 (c)13,2 (d)10,5

• By the help of option 12,3 is right answer because
  12+3=15
  gm of 12,3=6
  am of 12,3 =7.5
  20% of am=1.5
  hence gm is 20% lower than am.
  so, it satisfy the whole condition.
  
• 9 years agoHelpfull: Yes(15) No(1)
• ans: 12,3
  the arithmetic mean is (12+3)/2 = 7.5
  the geometric mean is sqrt(12*3)=6
  the 20% of arithmetci mean is 1.5
  therefore geometric mean is 20% less than the arithmetic mean
• 9 years agoHelpfull: Yes(7) No(0)
• answer is b i.e. 12,3
• 9 years agoHelpfull: Yes(3) No(6)
• X+Y=15
  SQRT(xy) =.8((X+Y)/2)
  XY=36 using both eqn ans is 12,3
• 9 years agoHelpfull: Yes(1) No(0)
• correct answer is 12,3
  EXPLANATION:
  consider two number a and b
  if we check option 2
  a =12 b=3
  a+b=12+3=15
  arithmetic mean =a+b/2
  12+3/2=15/2=7.5
  geometric mean =root(a*b)
  =root(36)=6
  accon to question geometric mean is 20 % less than aritmetic
  so 7.5*80/100=6
  
  
• 8 years agoHelpfull: Yes(1) No(0)
• correct ans= b(12,3)
• 7 years agoHelpfull: Yes(1) No(0)
• let us assume 2 no. x and y
  AM=(x+y)/2
  GM^2=xy
  
  x+y=15(given
  
  Am=15/2=7.5
  Gm=Am-20% of AM
  =7.5- (20*7.5/100)
  =7.5-1.5=6
  Gm=6;
  Gm^2=36
  xy=36
  x+y=15;
  solving both we get x=12 and y=3
• 6 years agoHelpfull: Yes(1) No(0)
• correct answer is b 12,3 . direct arun sharma book question
• 8 years agoHelpfull: Yes(0) No(1)
• correct answer is b 12,3 . direct arun sharma book question
• 8 years agoHelpfull: Yes(0) No(0)
• correct answer is b 12,3 . direct arun sharma book question
• 8 years agoHelpfull: Yes(0) No(0)
• correct answer is b 12,3 . direct arun sharma book question
• 8 years agoHelpfull: Yes(0) No(0)
• correct answer is b 12,3 . direct arun sharma book question
• 8 years agoHelpfull: Yes(0) No(0)
• go through the option consider option(b)
  gm of 12,3=sqrt of(12,3)=6
  am of 12,3=(12+3)/2=7.5
  20%of am=1.5
  gm=7.5-1.5=6
• 7 years agoHelpfull: Yes(0) No(0)
• let, 1st no=a then 2nd no=15-a
  power 1/2 of a(15-a)=15/2-15/2*20%
  by solving we get a=12 ,3 and b=3,12
• 6 years agoHelpfull: Yes(0) No(0)