Question

A number consists of three digits in GP.If the sum of twice middle digit by 1 and the sum of the left hand and middle digits is two third of the sum of the middle and right hand digits, then the number is​

Answer 1

Answer:

Let the three digits be a,ar,ar

2

then number

100a+10ar++ar

2

⋯(1)

Given, a+ar

2

=2ar+1

⇒a(r

2

−2r+1)=1

⇒a(r−1)

2

=1⋯(2)

Also given, a+ar=

3

2

(ar+ar

2

)

⇒3+3r=2r+2r

2

⇒2r

2

−r−3=0

⇒(r+1)(2r−3)=0

∴r=−1,3/2

for r=−1,a=

(r−1)

2

1

=

4

1

∈

/

1 ∴r



=1

for r=3/2,a=

(

2

3

−1)

2

1

=4 {From(2)}

From (1), number is 400+10.4.

2

3

+4.

4

9

=469

and Series

157 Qs

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