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Divide 40 into four parts such that the ratio of product of extremes to the product of means is 3 . What is progression and solution of question

Divide 40 into four parts such that the ratio of product of extremes to the product of means is 3 . What is progression and solution of question

Grade:10

1 Answers

Arun
25763 Points
3 years ago
Dear Sandesh
 
Let the four parts be a-3d, a-d, a+d, a+3d.
Then, 
a-3d+ a-d+ a+d+ a+3d = 40
4a=40
a = 10
 
Thus, the four parts are 10-3d, 10-d, 10+d, 10+3d.
 
Now, it is also given that:
ratio of product of extremes to the product of means is 2:3
 
Thus, 
(10-3d)(10+3d)/(10-d)(10+d) = 2/3
100-9d2/100-d2 = 2/3
300-27d2 = 200-2d2
25d= 100
d= 4
d = 2 or -2
 
Thus, the four parts (which are in AP) are 
4, 8, 12, 16
or
16, 12, 8, 4
 
Regards
Arun (askIITians forum expert)

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