First slide

Means - A.M/G.M/H.M

Question

Between two numbers whose sum is 13/6 , an even number of A.M’s are inserted , the sum of these means exceeds the number of means by unity, then find the number of means

Moderate

A

10
B

12
C

13
D

15

Solution

Let a and b be two numbers and 2n, A.M’s are inserted between a and b, then
$\begin{aligned} f r o m t h e g i v e n d a t a w e c a n w r i t e, \frac{2 n}{2} (a + b) = 2 n + 1 ∵ (a + b = \frac{13}{16}) \\ \to \underset{}{\underset{}{n}} (\frac{13}{6}) = 2 n + 1 \Rightarrow n = 6 \\ ∴ Number of mean = 12 . \end{aligned}$

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