## Task 1 - V10731

In the GDR, the number of manufactured cameras increased by 10% in 1959 compared to 1958 and amounted to approximately 558,000 units. How many units were produced in 1958?

Fritz calculates: "558,000 minus 10% of that, which is 55,800. Therefore, in 1958: 558,000 - 55,800 = 502,200 units were produced."

a) What mistake did Fritz make?

b) How should it be calculated correctly, and what is the result?

c) The number of manufactured television sets increased by 61% from 1958 to 1959 and amounted to 290,000 units in 1959. How many units were produced in 1958?

d) How large is the deviation in this case compared to the result Fritz obtained with his incorrect calculation?
a) The error lies in the fact that the $10 \%$ was applied to the percentage value of 1959 and not to the base value of 1958.

b) An increase of 10 \% means that the percentage value $P$ of 1959 corresponds to $110 \%$ of the base value $G$ of 1958, i.e.

$$
\frac{P}{G}=\frac{110}{100} \rightarrow \frac{558000}{G}=1.1 \quad \rightarrow \quad G=\frac{558000}{1.1}=507272
$$

In 1958, 507272 cameras were produced.

c) Analogous to task b), we get

$$
\frac{P}{G}=\frac{161}{100} \rightarrow \frac{290000}{G}=1.61 \quad \rightarrow \quad G=\frac{290000}{1.61}=180124
$$

In 1958, 180124 television sets were produced.

d) With the incorrect calculation, it would result in: $290000-0.61 \cdot 290000=113100$. The deviation would consequently be 67024 television sets.