Question

Divide 207 in three parts, such that all parts are in A.P. and product of two smaller parts will be 4623.

Answer 1

Let the three numbers be a – d, a and a + d.

According to the question,
$$\begin{gathered} \left(a-d\right)+a+\left(a+d\right)=207 \\ \Rightarrow 3a=207 \\ \Rightarrow a=69 \end{gathered}$$

Also,
$$\begin{gathered} \left(a-d\right)a=4623 \\ \Rightarrow \left(69-d\right)\left(69\right)=4623 \\ \Rightarrow 69-d=\frac{4623}{69} \\ \Rightarrow 69-d=67 \\ \Rightarrow 69-67=d \\ \Rightarrow d=2 \end{gathered}$$

Hence, the three numbers are 67, 69 and 71.