Question

sum of the 1/6 of a number and 3/8 the same number is 55 find the number
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Answer 1

Answer:

Let the three numbers in G.P. be a,ar and ar

2

From the given condition

a+ar+ar

2

=56

⇒a(1+r+r

2

)=56...(1)

Also given a−1,ar−7,ar

2

−21 forms an A.P.

∴(ar−7)−(a−1)=(ar

2

−21)−(ar−7)

⇒ar−a−6=ar

2

−ar−14

⇒ar

2

−2ar+a=8

⇒a(r

2

+1−2r)=8

⇒a(r−1)

2

=8...(2)

Using (1) and (2)

⇒7(r

2

−2r+1)=1+r+r

2

⇒7r

2

−14r+7−1−r−r

2

=0

⇒6r

2

−15r+6=0

⇒6r

2

−12r−3r+6=0

⇒6r(r−2)−3(r−2)=0

⇒(6r−3)(r−2)=0⇒r=2,

2

1

When r=2, a=8

And three numbers in GP are 8,16 32.

When r=

2

1

, three numbers in G.P. are 32,16 and 8.

Thus in either case, the three required numbers are 8,16 and 32.

Answer 2

Answer:

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