If 3 numbers are in the ratio of 3:2:5 such that sum of their squares is equal to 1862. what is the middle number?
Option
a) 25
b) 14
c) 30
d) 34

• Let the numbers are 3x, 2x, 5x
  Now,
  (3x)^2 + (2x)^2 + (5x)^2 = 1862
  => x^2 = 49
  => x = 7
  middle number is 2x = 2 * 7 = 14
• 10 years agoHelpfull: Yes(38) No(0)
• Let numbers be 3x, 2x, 5x
  Now 9x2+4x2+25x2=1862
  X2=1862/38
  X=7
  So, second number=2*7=14
  
• 9 years agoHelpfull: Yes(10) No(1)
• let the no.s be 3x, 2x and 5x
  
  given: (3x)^2+(2x)^2+(5x)^2=1862
  
  Solving above equation, we get
  
  x=7
  
  so, middle no. i.e., "2x=14"
• 9 years agoHelpfull: Yes(3) No(0)
• From options
  b) 14
  3 : 2 : 5
  21 : 14 : 35
  21^2 + 14^2 +35^2
  441 + 196 + 1225 = 1862
  
  Alternate method
  middle number is given
  if 2 parts = 25 / 14 / 30 /34
  then 1 part is 12.5 / 7 / 15 / 17
  
  1862 must be divisible by any of the above
  
  1862 is not divisible by 12.5 so option a is not possible
  " " is divisible by 7 so option b
• 10 years agoHelpfull: Yes(2) No(7)
• 14
  (3x)^2+(2x)^2+(5x)^2=1862
  x^2=49
  x=7
  2*x=14
• 10 years agoHelpfull: Yes(2) No(0)
• let the no.be x
  so the ratio will be
  3x:2x:5x
  Sum of their squares 9(x)^2 + 4(x)^2 + 25(x)^2 = 1862
  38(x)^2=1862
  x=7, so the middle no will be 7*2=14
  Ans:-14
• 10 years agoHelpfull: Yes(2) No(0)
• b) 14
  (3x)^2+(2x)^2+(5x)^2=1862
  x=7
  
• 9 years agoHelpfull: Yes(2) No(1)
• b)=14
  let the num be x
  9x^2+4x^2+25x^2=1862
  x^2=49===>x=7
  then middle num=7*2=14
• 9 years agoHelpfull: Yes(2) No(0)
• the 3 nos are in the ratio 3:2:5
  so let the nos be 3x 2x 5x
  (3x)^2+(2x)^2+(5x)^2=1862
  9x^2+4x^2+25x^2=1862
  38x^2=1862
  x=7
  the middle term is 2x=2*7=14
  therefore b is the ans
• 9 years agoHelpfull: Yes(2) No(0)
• 30
  
  15*2=30
  1583=45
  15*5=75
  The sum of squares is 1862
  45^2+30^2+75^2=1862
• 10 years agoHelpfull: Yes(1) No(7)
• The answer for this question is 14.
• 9 years agoHelpfull: Yes(0) No(1)
• As 3 numbers are in the ratio of 3:2:5,
  Let the numbers are 3x, 2x, 5x
  Now, so the ratio will be
  3x:2x:5x
  As sum of their squares is equal to 1862
  
  Now,
  (3x)^2 + (2x)^2 + (5x)^2 = 1862
  => x^2 = 49
  
  => x = 7
  
  middle number is 2x = 2 * 7 = 14
  b) 14
  
  
• 9 years agoHelpfull: Yes(0) No(0)
• suppose no. is 3x,2x,5x
  ans is b
• 9 years agoHelpfull: Yes(0) No(1)
• let the num be x
  9x^2+4x^2+25x^2=1862
  x^2=49===>x=7
  then middle num=7*2=14
• 9 years agoHelpfull: Yes(0) No(0)
• let the ratio common factor equals to x.thus the nos are 3x,2x,5x
  thus 38 x^2=1862(as sum of the squares=1862)
  thus x=14
• 9 years agoHelpfull: Yes(0) No(0)
• x=7*2=14 is da ans
• 8 years agoHelpfull: Yes(0) No(0)
• let the numbers are 3x,2x,5x
  then (9x^2+)+4x^2+25x^2=1862
  x^2=49
  x=7
  middle number=2x=14
• 8 years agoHelpfull: Yes(0) No(0)
• check with the options. if u take 14 as middle number
  the ratio will be 21:14:35
  check sum of squares of these numbers will gives u 1862
  remaining will not give
  so,answer is 14
• 8 years agoHelpfull: Yes(0) No(0)
• root49*2=14
• 8 years agoHelpfull: Yes(0) No(0)
• root(1862/(3^2+2^2+5^2))= root(1862/38)= 7
  middle no= 7*2= 14
• 8 years agoHelpfull: Yes(0) No(0)
• 3:2:5
  so sum of squares of these numbers is (3x)(3x)+(2x)(2x)+(5x)(5x)=1862
  38(x^2)=1862
  x^2=1862/38
  x^2=49 therefore x=7
  second num is 2(x)=2(7)=14
  
  ans is (b)
• 8 years agoHelpfull: Yes(0) No(0)
• 3x,2x,5x
  9x^2+4x^2+25^2=1826
  x^2=49
  x=7
  middle no 2x=14
• 8 years agoHelpfull: Yes(0) No(0)
• 9+4+25=38
  4/38*1862=196
  root of 196=14 Ans
• 8 years agoHelpfull: Yes(0) No(0)
• Let the three nos. be 3x , 2x & 5x
  So a.t.q,
  (3x)^2 + (2x)^2 +(5x)^2 =1862
  x^2 (38)= 1862
  x^2=1862/38
  x^2=49
  x=7
  
  therefore, the middle no. is 2x=2*7=14
  ans. is 14
• 8 years agoHelpfull: Yes(0) No(0)
• 14
  9x^2+4x^2+25^2=1862
  38x^2=1862
  x=7
  middle number=7*2=14
  
• 8 years agoHelpfull: Yes(0) No(0)
• Take b)14
  then 21,14,35 are three numbers then squares sum = 1862.
• 8 years agoHelpfull: Yes(0) No(0)
• b is the answer
  3:2:5 their sum squares =1862
  multiply with 7 by each=21:14:35
  21*21=441,14*14=196,35*35=1225
  441+196+1225=1862 so mid value=14
  
• 8 years agoHelpfull: Yes(0) No(0)
• 1862/38=49
  x=7
  2*7=14
• 6 years agoHelpfull: Yes(0) No(0)