If an arithmetic mean between $3 a$ and $8 + 5 a$ is $10 a + 8$ , then find $a$ .

- 5

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- \frac{1}{3}

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- \frac{2}{3}

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- 3

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Solution

The correct option is C $- \frac{2}{3}$
Given that arithmetic mean of $3 a$ and $8 + 5 a$ is $10 a + 8$
Therefore, $\frac{3 a + 8 + 5 a}{2} = 10 a + 8$
$\Rightarrow 8 a + 8 = 20 a + 16$
$\Rightarrow 12 a = 8 - 16$
$\Rightarrow 12 a = - 8$
$\Rightarrow a = - \frac{2}{3}$

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