Practice Test Discussion

The average of 30 numbers is 40 and that of either 40 numbers is 30. The average of all the numbers is ?

34.5

34 $\frac{2}{7}$

None of these

Explanation

According to the question,

$n_{1} = 30, A_{1} = 40, n_{2} = 40, A_{2} = 30$

We know the formula

Weighted average(Aw)= $\frac{n_{1} A_{1} + n_{2} A_{2}}{n_{1} + n_{2}}$

Average of all the 70 numbers

$= \frac{30 \times 40 + 40 \times 30}{30 + 40} = \frac{2400}{70} = 34 \frac{2}{7}$

Hence, Option D is correct.

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