Question

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

Answer 1

Let the required parts of 24 be (a – d), a and (a + d) such that they are in AP.

Then (a – d) + a + (a + d) = 24 

⇒ 3a = 24 

⇒ a = 8 

Also, (a – d) . a . (a + d) = 440

⇒ a(a² – d²) = 440

⇒ 8(64 – d²) = 440

⇒ d² = 64 – 55 = 9

⇒ d = ±3

Thus, a = 8 and d = ±3

Hence, the required parts of 24 are (5, 8, 11) or (11, 8, 5).