Question

A number 36 is divided into four parts that are in A.P. such that the ratio of product of first and fourth part to the product of second and third part is 9:10. The sum of second and fourth part is not divisible by​

Answer 1

Given :- A number 36 is divided into four parts that are in A.P. such that the ratio of product of first and fourth part to the product of second and third part is 9:10.

To Find :- The sum of second and fourth part is ?

Solution :-

Let us assume that, the four parts are (a - 3d) , (a - d) , (a + d) and (a + 3d) .

so,

→ a - 3d + a - d + a + d + a + 3d = 36

→ 4a = 36

→ a = 9

A/q,

→ (9 - 3d)(9 + 3d) / (9 - d)(9 + d) = 9/10

→ (81 - 9d²) / (81 - d²) = 9/10

→ 9(9 - d²)/(81 - d²) = 9/10

→ 90 - 10d² = 81 - d²

→ 90 - 81 = 10d² - d²

→ 9 = 9d²

→ d² = 1

→ d = ± 1

when d = + 1,

→ sum of 2nd and fourth part = 9 - d + 9 + 3d = 18 + 2d = 20

when d = -1 ,

→ sum of 2nd and fourth part = 9 - d + 9 + 3d = 18 + 2d = 18 - 2 = 16

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