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,
⇒ Sum of these parts = 207
⇒ a – d + a +a +d = 207
⇒ 3a = 207
So, a = 69
Given that, product of the two smaller parts = 4623
⇒ a (a - d) = 4623
⇒ 69 (69 - d) = 4623
⇒ 69 - d = 67
⇒ d = 69 - 67 = 2
So, the first part = a – d = 69 – 2 = 67,
Second part = a = 69
Third part = a + d = 69 + 2 = 71