Question

Divide 72 into four eqal parts which are in ap such that the

Answer 1

pls give me full question
the four equal part of 72 is 18

Answer 2

The required parts are 9, 15, 21, 27 or 27, 21, 15, 9 which are in A.P.

Complete question:

Divide 72 in four parts which are in A.P. such that the ratio of the product of their extremes (1st and 4th ) to the product of means (2nd and 3rd) is 27/35. Find the four parts.

Step-by-step explanation:

Let the four parts of 72 which are in A.P. be

a - 3d, a - d, a + d and a + 3d.

According to the question,

(a - 3d) + (a - d) + (a + d) + (a + 3d) = 72

⇒ a - 3d + a - d + a + d + a + 3d = 72

⇒ 4a = 72

⇒ a = 18

Then the four parts become

18 - 3d, 18 - d, 18 + d and 18 + 3d.

Again, according to the question,

1st part × 4th part : 2nd part × 3rd part = 27 : 35

⇒ (18 - 3d) × (18 + 3d) : (18 - d) × (18 + d) = 27 : 35

⇒ (324 - 9d²) : (324 - d²) = 27 : 35

⇒ 35 × (324 - 9d²) = 27 × (324 - d²)

⇒ 11340 - 315d² = 8748 - 27d²

⇒ 315d² - 27d² = 11340 - 8748

⇒ 288d² = 2592

⇒ d² = 9

⇒ d = ± 3

So, the required four parts which are in A.P. are

18 - 3 × 3, 18 - 3, 18 + 3, 18 + 3 × 3

i.e., 18 - 9, 18 - 3, 18 + 3, 18 + 9

i.e., 9, 15, 21, 27

or, 18 - 3 × (- 3), 18 - (- 3), 18 + (- 3), 18 + 3 × (- 3)

i.e., 18 + 9, 18 + 3, 18 - 3, 18 - 9

i.e., 27, 21, 15, 9