Question

Let ${}^{\prime }{n}^{\prime }A.M^{\prime }s$ be inserted between $x,2y$ and $2x,y$. If $k^{th}A.M.$ of both the sets are equal, then which of the following is true

• A. $ky=(n-k)x$
• B. $ky=(n-k+1)x$
• C. $ky=(n+k)x$
• D. $ky=(n+k-1)x$

Answer 1

The correct option is B $ky=(n-k+1)x$

Given, $x+k\left(\frac{2y-x}{n+1}\right)=2x+k\left(\frac{y-2x}{n+1}\right)$
$\Rightarrow k\left(\frac{y+x}{n+1}\right)=x\Rightarrow ky+kx=(n+1)x\Rightarrow ky=x(n+1)-kx\Rightarrow ky=(n-k+1)x$