24. Divide 40 into four parts, which are in A.P. such
ratio of product of extremes
to the product of means is
3
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MATHS
Divide 40 into four parts, which are in A.P. such that ratio of product of extremes is to the product of means is 2:3.
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ANSWER
Let the four parts of 40 are
a−3d,a−d,a+d,a+3d
then , a−3d+a−d+a+d+a+3d=40
⇒4a=40
⇒a=10
Now ,
(a−d)(a+d)
(a−3d)(a+3d)
=
3
2
⇒
a
2
−d
2
a
2
−9d
2
=
3
2
⇒
(10)
2
−d
2
(10
2
)−9d
2
=
3
2
⇒
100−d
2
100−9d
2
=
3
2
⇒300−27d
2
=200−2d
2
⇒100=25d
2
⇒d
2
=4
⇒d=±2
If d=2,a=10
then four parts of 40 are
10−3×2,10−2,10+2,10+3×2
=4,8,12,16
If d=−2,a=10 then , four parts are
10−3×−2,10−(−2),10−2,10+3(−2)
=16,12,8,4
hence four parts of 40 are 4,8,12,and16
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