Question 19

Split 69 into three parts such that they are in an arithmetic progression and the product of the two smaller parts is 483.

Let the terms in the arithmetic progression be $$(a-d)$$, $$a$$, $$(a+d)$$ where $$a$$ is the first term and $$d$$ is the common difference.

We are given that, $$a - d + a + a +d = 69$$ $$\Rightarrow$$ $$a=23$$

Since $$a$$ and $$a-d$$ are the lowest terms in the arithmetic progression, $$a(a - d) = 483$$, putting $$a=23$$ in the equation we get $$d=2$$.

Hence , the terms are $$21$$, $$23$$ and $$25$$.

Option D is correct.

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