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,

\[\left( a - d \right) + a + \left( a + d \right) = 207\]

\[ \Rightarrow 3a = 207\]

\[ \Rightarrow a = 69\]

Also,

\[\left( a - d \right)a = 4623\]

\[ \Rightarrow \left( 69 - d \right)\left( 69 \right) = 4623\]

\[ \Rightarrow 69 - d = \frac{4623}{69}\]

\[ \Rightarrow 69 - d = 67\]

\[ \Rightarrow 69 - 67 = d\]

\[ \Rightarrow d = 2\]

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