Latest Elitmus Aptitude Question SOLUTION: 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

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(#M40019633) ELITMUS question Keep an EYE

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

Asked In Elitmus Devanshu (10 years ago)

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Maharaja T N  (10 years ago)

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

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TEJ PRAKASH TEWARI  (10 years ago)

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

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