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Divide 124 into 4 parts which is in progression such that the product of the 1st and the 4th part is 128 less than the product of the 2md and the 3rd part

Divide 124 into 4 parts which is in progression such that the product of the 1st and the 4th part is 128 less than the product of the 2md and the 3rd part

Grade:10

1 Answers

Arun
25750 Points
6 years ago
Dear students
Let the 4 parts be
a- 3d, a -d, a+d, a+ 3d
Sumnof all of this is 124
Hence
4a = 124
a = 31
(a -3d) (a+3d) = (a-d)(a+d) -128
a² - 9d² = a² - d² -128
8d² = 128
d² = 128/8 = 16
d = +4 or -4
Hence if d = +4
Then numbers are
19, 27, 35, 43
 
If we take d = -4, we get aame numbers but in reverse order.
 
Regards
Arun (askIITians forum expert)

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