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Average of 12 numbers is 48 average of the first 7 numbers is 60 and the average of last 4 numbers is 22 then the eighth number is____.
Given:
Average of 12 numbers is 48 average of the first 4 numbers is 60 and the average of last 7 numbers is 22.
To do:
We have to find the eighth number.
Solution:
Let the eighth number be $x$.
Average of 12 numbers$=\frac{Sum\ of\ 12\ numbers}{12}$
$48=\frac{Sum\ of\ 12\ numbers}{12}$
Sum of 12 numbers$=48\times12=576$
Sum of 12 numbers$=$ Sum of first 7 numbers $+$ Eighth number $+$ Sum of last 4 numbers
Average of first 7 numbers$= \frac{Sum\ of\ first\ 7\ numbers}{7}$
$60=\frac{Sum\ of\ first\ 7\ numbers}{7}$
Sum of first 7 numbers $=60\times7=420$.
Average of last 4 numbers$= \frac{Sum\ of\ last\ 4\ numbers}{4}$
$22=\frac{Sum\ of\ last\ 4\ numbers}{4}$
Sum of last 4 numbers $=22\times4=88$.
Therefore,
$576=420+Eighth\ number+88$
Eighth number$=576-508=68$
Therefore, the eighth number is 68.
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