Question

When $10$ is subtracted from all the observations, the mean is reduced to $60\%$ of its value. If $5$ is added to all the observations, then the mean will be

Answer 1

Let the original mean is $\overline{x}$
If $10$ is subtracted from all the observations, then the new mean is $60\%\overline{x}=\frac{3}{5}\overline{x}$

Also, when $10$ is reduced from every observations, then new mean is $\overline{x}-10$, so
$\overline{x}-10=\frac{3}{5}\overline{x}\Rightarrow \overline{x}=25$

Now, $5$ is added to all the observations, then the mean
$=\overline{x}+5=30$