The average of x numbers is y and average of y numbers is x. Then the average of all the numbers taken together is:

The average of x numbers is y and average of y numbers is x. Then the average of all the numbers taken together is:
[A]\frac{xy}{x+y}
[B]\frac{x+y}{2xy}
[C]\frac{x^{2}+y^{2}}{x+y}
[D]\frac{2xy}{x+y}

\mathbf{\frac{2xy}{x+y}}
Sum of x numbers = xy
Sum of y numbers = xy
∴ Required Average = \frac{xy+xy}{x+y} = \frac{2xy}{x+y}
Hence option [D] is the right answer.

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