The mean of 30 given numbers, when it is given that mean of 10 of them is 12 and the mean of the remaining 20 is 9

10`

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\frac{21}{2}

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Solution

The correct option is A 10`
Let x be the mean of 30 numbers and xi denote the number where $1 \leq x \leq 30$
Mean of 10 numbers = 12.
$\Rightarrow \frac{x_{1} + x_{2} + x_{10}}{10} = 12$
$\Rightarrow x_{1} + x_{2} + . . . . . . . + x_{10} = 120$ _________ (1)
Mean of remaining 20 numbers = 9.
$\Rightarrow \frac{x_{11} + x_{12} + . . . . . . + x_{30}}{20} = 9$
$\Rightarrow x_{11} + x_{12} + . . . . . . . x_{30} = 180$ ___________ (2)
$∴ x = \frac{x_{1} + x_{2} + . . . . . . x_{30}}{30}$
$= \frac{x_{1} + x_{2} + . . . . . + x_{10} + x_{11} + . . . . + x_{30}}{30}$ [from (1)and (2)]
$= \frac{120 + 180}{30}$
$= \frac{300}{30}$
= 10

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