If the decimal number 120 when expressed to the base a,b and c equals 60,80,100 respectievely ,then which of the following statement is true?
a) a,b,c are in geometric progression
b) a,b,c are in arithmetic progression
c) a,b,c are in harmonic progression
d) a-b-c=1

• 60 is obtained when base value of 120 is 20 -> a
  80 is obtained when base value of 120 is 15 -> b
  100 is obtained when base value of 120 is 12 -> c
  Now 20,15,12 are in Harmonic Progression..
  Condition for HP..
  (1/b)-(1/a)=(1/c)-(1/b)
  here
  (1/15)-(1/20)equals(1/12)-(1/15)
  So (C) is correct option
• 11 years agoHelpfull: Yes(21) No(2)
• 120 base 10= 60 base a i.e. a=(120/60)*10 =>a=20
  120 base 10=80 base b i.e. b=(120/80)*10 =>b=15
  120 base 10= 100 base c i.e. c=(120/100)*10 =>c=12
  We can see clearly it is neither in A.P. nor in G.P. also not satisfying last option
  Now for H.P. b=2ac/(a+c)
  2*20*12/32=15
  condition satisfied
  Ans. c) a,b,c are in harmonic progression
  
• 11 years agoHelpfull: Yes(8) No(2)