Latest Elitmus Aptitude Question SOLUTION: 35,80,135 are three numbers in the bases a,b & c resp.35,80,& 135 correspond to 120 in base 10 system. a,b,c are in which progression?

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(#M40017726) ELITMUS question Keep an EYE

35,80,135 are three numbers in the bases a,b & c resp.35,80,& 135 correspond to 120 in base 10 system. a,b,c are in which progression?

Asked In Elitmus PRASAD REDDY KUNDURI (11 years ago)

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Anurag Srivastava  (11 years ago)

is anything is not missing there PRASAD REDDY KUNDURI ???

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P.Someshwar Reddy  (10 years ago)

given that base of 35 is a, base of 80 is b and base of 135 is c and they all are equal to 120 in decimal number system, that is base 10.
(35)a=(80)b=(135)c=(120)10
then 120 base 10 is actually 120 itself
equate 35 base a to 120
i.e. (35)a=120
then by conversion the above can be written as
3a+5=120 -> 3a=120-5 -> 3a=115 -> a=115/3 -> a=38.33333
again equate 80 base b to 120
i.e. (80)b=120
then by conversion the above can be written as
8b+0=120 -> 8b=120 -> b=15
once again equate 135 base c to 120
i.e. (135)c=120
then by conversion the above can be written as
c^2+3c+5=120 -> c^2+3c-115=0
calculate roots for c^2+3c-115=0 take the negative root
that is "c" could be equal to -12.32
Now compare the values of a,b,c
a=38.3, b=15, c=-12.3
difference between them is equal
so, the roots are in Arithmetic progression

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