Latest Elitmus Aptitude Question SOLUTION: If a, b and c are forming increasing terms of G.P. , r is the common ratio then find the minimum value of (c-b), given that (log a+log b+log c)/log 6 =6.Note that r can be any real

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(#M40153877) ELITMUS Numerical Ability question Quantative Keep an EYE

If a, b and c are forming increasing terms of G.P. , r is the common ratio then find the minimum value of (c-b), given that (log a+log b+log c)/log 6 =6.Note that r can be any real no.

Asked In Elitmus ANIL KUMAR (8 years ago)

Unsolved Read Solution (7)

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Read Solution (7) :

Abhishek  (8 years ago)

a,b,c are in GP so let the first term of gp is a with common ration r.
then b=ar
c=ar^2
Now (loga+logb+logc)/log6=6
logabc (base 6) =6
abc=6^6
put the value of a,b,c in gp format
a.ar.ar^2=6^6
a^3r^3=6^6
ar=6^2
ar=36;
that is b=36.
Now we've been asked minimum value of (c-b)
there was 4 option
A).36 b).24 c). 18 D). 12
lets take c-b =18
you will get c= b+18 =>54
now b=ar=36
r=54/36
so r =3/2
then b=ar=36
a.3/2=36
a=24
now we have gp as 24,36,54
and c-b=18 ( i would recommend you to solve this by using option A, B also. Although option c is also not true)
Now lets go with option 4
lets take c-b=12
c=12+b;
c=48
r=c/b;
r=48/36;
r=4/3;
b=ar=36;
a.4/3=36;
a=27;
Now the gp we have is the 27,36,48
and the differnce between c and b is 12 that is minimum
hence the option is D

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Anjali Sadhukhan  (8 years ago)

those whose ans are not belong to those options are wrong ..A).36 b).24 c). 18 D). 12 ...as those were the given options..

Is this solution Helpfull? Yes (1) | No (2)  

Prateek Gupta  (4 years ago)

180
after calculations ar=36
for gp a,ar,ar^2
6,6^2,6^3
ar(r-1)=36(6-1)=180

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Appala Naidu Gollu  (8 years ago)

ans can be 6

Is this solution Helpfull? Yes | No (1)  

amrita.ece09@yahoo.in  (8 years ago)

please explain!!!

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Spartan  (8 years ago)

Answer is 30

Is this solution Helpfull? Yes | No (2)  

Shubbam  (5 years ago)

a,b,c are in G.P. so let the first term of G.P. =
a
r
, and common ratio = r.
Therefore, a =
a
r
, b =
a
, c =
a
r

Given,
log
a
+
log
b
+
log
c
log
6
=
6

⇒
log
a
b
c
log
6
=
6

⇒
log
6
a
b
c
=
6
⇒
a
b
c
=
6
6

put the value of a,b,c in gp format
⇒
a
r
×
a
×
a
r
=
6
6

⇒
a
3
=
6
6
⇒
a
=
36

Now a =
36
r
, b = 36, c = 36r.
We have to find the minimum value of c - b = 36r - 36.
r can be any number. So for r < 0, we get c - b negative.
When r = 1, c - b = 0
But none of the options are not representing it.
From the given options, r = 4/3, then c = 48. So option d satisfies this.

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