Question

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

Answer 1

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