Q. 8

Divide 24 in three parts such that they are in AP and their product is 440.

Answer :

Let 24 be divided in numbers which are in AP as (a - d), a, (a + d).

Now, sum of the numbers = 24


(a - d) + a + (a + d) = 24


3a = 24


a = 8


Now, product of the numbers = 440


(a - d) × a × (a + d) = 440


a3 - ad2 = 440


Put the value of a, we get,


512 - 8d2 = 440


8d2 = 512 - 440 = 72


d2 = 9


d = � 3


If d = 3, then the numbers are 5, 8, 11.


If d = - 3, then the numbers are 11, 8, 5.


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