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Q.

Three numbers form a H.P. the sum of the numbers is 11 and the sum of their reciprocals is 1. Then one among those numbers is

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a

\frac{1}{2}

b

\frac{1}{6}

c

2

d

3

answer is A.

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Detailed Solution

Let

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

are in H.P

Given that,

Sum of the reciprocal is 1

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

$∴ \frac{1}{a} = 3$

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Three numbers form a H.P. the sum of the numbers is 11 and the sum of their reciprocals is 1. Then one among those numbers is