Question

the average of 15 numbers is equal to the average of the 16 numbers. hence the 16th number is​

Answer 1

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Answer 2

Given,

Average of 15 numbers = Average of 16 numbers

To Find,

The value of the sixteenth number.

Solution,

Average of fifteen numbers = $\frac{sum of 15 numbers}{15}$

Assume sum of fifteen numbers is $S$

⇒Average of fifteen numbers = $\frac{S}{15}$

Average of sixteen numbers = $\frac{sum of 16 numbers}{16}$

⇒$\frac{Sum of 15 numbers+ 16th number}{16}$

Assume sixteenth number as $x$

⇒$\frac{S+ x}{16}$

Average of 15 numbers = Average of 16 numbers

⇒$\frac{S}{15} =\frac{S+x}{16}$

⇒$\frac{16S}{15} = S+x$

⇒$x = \frac{16S}{15} - S = \frac{16S-15S}{15} = \frac{S}{15}$

∴ $x = \frac{S}{15}$

Henceforth, the value of the sixteenth number is equal to the average of 15 numbers, $\frac{S}{15} .$