Split 207 into three parts such that these are in AP and the product of two smaller part is 4623

Split 207 into three parts such that these partsare in A.P. and the productof the two smaller parts in 4623. 

Let the tree parts in A.P nbe (a-d), a and (a+d) Then, `(a-d)+a+(a+d)=207` 

`⇒ 3a=207`

`⇒a=69` 

It is given that 

`(a-d)xxa=4623`

`⇒(69-d)xx69=4623`

`⇒69-d=67`

`⇒d=2`

`⇒ a=69 and d=2`

Thus, We have 

`a-d=69-2=67`

`a=69`

`a+d=69+2=71`

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

Concept: Simple Applications of Arithmetic Progression

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Question 12 Split 207 into three parts such that these are in AP and the product of the two smaller parts is 4623 .

Solution

Let the three parts of the number 207 be (a - d), a and (a + d), which are in AP.
Now, by given condition,
$\Rightarrow$ Sum of these parts = 207
$\Rightarrow$ a – d + a +a +d = 207
$\Rightarrow$ 3a = 207
So, a = 69
Given that, product of the two smaller parts = 4623
$\Rightarrow$ a (a - d) = 4623
$\Rightarrow$ 69 (69 - d) = 4623
$\Rightarrow$ 69 - d = 67
$\Rightarrow$ d = 69 - 67 = 2
So, the first part = a – d = 69 – 2 = 67,
Second part = a = 69
Third part = a + d = 69 + 2 = 71