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

Question

Philoid · Accepted 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.