Question

Split 207 into three parts such that these parts are in A.P. and the product of the two smaller parts in 4623.

Answer 1

Let the three parts in A.P. be (a – d), a and (a + d)

Then, (a – d) + a + (a + d) = 207 

`\implies` 3a = 207

`\implies` a = `207/3` = 69

It is given that 

(a – d) × a = 4623

`\implies` (69 – d) × 69 = 4623

`\implies` 69 – d = `4623/69` = 67

`\implies` d = 69 – 67 = 2

`\implies` a = 69 and d = 2

Thus, we have 

a – d = 69 – 2 = 67

a = 69

a + d = 69 + 2 = 71

Thus, the three parts in A.P. are 67, 69 and 71.