Divide 28 into 4 parts in arithmetic progression, such that the ratio of product of first and third with the product of second and fourth is 8:15

• GIVEN:
  A, B , C, D are in A.P.
  A+B+C+D=28
  AC/BD=8/15
  all the above conditions are satisfied
  when A=4, B=6, C=8 and D=10
• 12 years agoHelpfull: Yes(4) No(2)
• solution is... 4,6,8,10
  explanation:
  assume four nos. in A.P. are a-d,a,a+d and a+2d.
  then by conditions 4a+2d=28 implies 2a+d=14
  and a*(a+2d)/((a+d)*(a-d))=8/15
  implies 15a^2+30ad=8a^2-8d^2
  implies 7a^2+30ad+8d^2=0
  or (a+4d)(7a+2d)=0
  implies a+4d=0 or 7a+2d=0
  now solving a+4d=0 and 2a+d=0 we have a=8 and d=-2
  which gives the required numbers as 4,6,,8,10.
• 12 years agoHelpfull: Yes(2) No(0)