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State True/False.

The numbers 5, 8 and 11 are the numbers we get after dividing 24 into three parts such that they are in AP and their product is 440.

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False

True

answer is A.

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Detailed Solution

Given that the numbers 5, 8 and 11 are the numbers on dividing 24 in three parts such that they are in A.P. and their product is 440.
Since, General Arithmetic Progression:

a − d, a

and

a + d

.
Let the required parts of 24 are

a − d, a

and

a + d

such that they are in A.P.
As the sum of these three numbers is 24.

∴ (a − d) + a + (a + d) = 24 ⇒ 3 a = 24 ⇒ a = 243 ⇒ a = 8

As the product of these three numbers is 440.

∴ (a − d) × a × (a + d) = 440

⇒ a a 2 − d 2 = 440

…… (1)
Putting the value of a=8 in equation (1):

⇒ 8 82 − d 2 = 440 ⇒ 64 − d 2 = 55 ⇒ d = 64 − 55 ⇒ d = ± 3

Take d=3, a=8 and determining the required parts of A.P.:

∴ (8 − 3), 8, and (8 + 3) ⇒ 5, 8, and 11

Take d=-2, a=8 and determining the required parts of A.P.:

∴ (8 + 3), 8, and (8 − 3) ⇒ 11, 8, and 5

Therefore, the required numbers are 5, 8 and 11 or 11, 8 and 5.
Thus, the given statement is true.
Hence, option (1) is correct.

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