​If the mean of x, y and z is K, then the mean of $$\frac{x}{y},\ 1,\ \frac{z}{y}$$​​

Correct option is B

Solution:

$$K = \frac{x + y + z}{3} \\\text{New mean: } \frac{1}{3} \left( \frac{x}{y} + 1 + \frac{z}{y} \right) = \frac{1}{3} \left( \frac{x + z + y}{y} \right) \\\ \\= \frac{1}{3} \cdot \frac{x + y + z}{y} = \frac{1}{3} \cdot \frac{3K}{y} = \frac{K}{y} \\\ \\\textbf{Final Answer:} \\\boxed{\frac{K}{y}}$$

$$K = \frac{x + y + z}{3} \\\text{New mean: } \frac{1}{3} \left( \frac{x}{y} + 1 + \frac{z}{y} \right) = \frac{1}{3} \left( \frac{x + z + y}{y} \right) \\\ \\= \frac{1}{3} \cdot \frac{x + y + z}{y} = \frac{1}{3} \cdot \frac{3K}{y} = \frac{K}{y} \\\ \\\textbf{Final Answer:} \\\boxed{\frac{K}{y}}$$

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