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