## Task 1 - 250811

a) Let $b$ be the number obtained when the number 30 is increased by $50 \%$.

By what percent must this number $b$ be reduced to obtain the number 30 again?

b) Check whether the statement found for the number 30 also holds for any positive number $a$ under the same problem statement!
a) If the number 30 is increased by $50 \%$, then we get $b=30+15=45$.

The number $b$ must be reduced by 15 to get 30 again. This value 15 is $\frac{1}{3}$ of 45, so the required percentage is $33 \frac{1}{3} \%$.

b) For any positive number $a$, the following applies: If $a$ is increased by $50 \%$, then we get

$$
b=a+\frac{a}{2}=\frac{3}{2} a
$$

This number must be reduced by $\frac{a}{2}$ to get $a$ again; $\frac{a}{2}$ is, however, one third of $\frac{3}{2} a$. Therefore, for any positive number $a$, the percentage sought in the same problem as in task a) is also $33 \frac{1}{3} \%$.