The mean of 15 numbers is 27. If each number is multiplied by 4,

Let the numbers be x1, x2,...x15
We know:

Mean $=\frac{\text { Sum of observa tions }}{\text { Number of observations }}$

Thus, we have:

$27=\frac{x_{1}+x_{2}+\ldots \ldots \ldots+x_{15}}{15}$

$\Rightarrow x_{1}+x_{2}+\ldots \ldots \ldots+x_{15}=405 \ldots \ldots \ldots$ (i)

After multiplication, the numbers become $4 x_{1}, 4 x_{2}, \ldots 4 x_{15}$

$\therefore$ New Mean $=\frac{4 x_{1}+4 x_{2}+\ldots \ldots+4 x_{15}}{15}$

$=\frac{4\left(x_{1}+x_{2}+\ldots \ldots+x_{15}\right)}{15}$

$=\frac{4 \times 405}{15} \quad[$ From $(\mathrm{i})]$

$=\frac{1620}{15}$

$=108$