The sum of three numbers in H.P is 26 and sum of their reciprocals is 38 , then the numbers are

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The sum of three numbers in H.P is 26 and sum of their reciprocals is $\frac{3}{8}$ , then the numbers are

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9, 12, 6

12, 8, 6

10, 12, 24

11, 9, 5

answer is C.

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Detailed Solution

Let three numbers in H.P are

\frac{1}{a - d}, \frac{1}{a}, \frac{1}{a + d}

$a - d + a + a + d = \frac{3}{8} \Rightarrow 3 a = \frac{3}{8} \Rightarrow a = \frac{1}{8}$

$\frac{1}{a - d} + \frac{1}{a} + \frac{1}{a + d} = 26 \Rightarrow \frac{1}{\frac{1}{8} - d} + 8 + \frac{1}{\frac{1}{8} + d} = 26 \Rightarrow d = \frac{1}{24}$

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