The warehouse received cement in bags weighing $25 \mathrm{~kg}$ and $40 \mathrm{~kg}$. There were twice as many smaller bags as larger ones. The warehouse keeper reported the total number of bags to the manager but did not specify how many of each. The manager assumed all bags weighed $25 \mathrm{~kg}$. Therefore, he multiplied the reported number of bags by 25 and documented the result as the weight of the cement delivery. Overnight, thieves stole 60 larger bags, leaving exactly the same number of kg of cement as the manager had recorded. How many kg of cement remained?

(L. Šimünek)
Thieves stole $60 \cdot 40=2400 \text{ kg}$. Before the theft, $15 \text{ kg}$ was missing from each large bag according to the documentation. The total undocumented weight equals the stolen weight, so the number of large bags delivered was

$$
2400: 15=160 \text{.}
$$

There were twice as many small bags, i.e., 320; in total, the delivery contained $160+320=480$ bags. The supervisor documented the weight as $480 \cdot 25=12000 \text{ kg}$. The amount of cement left corresponds to the documentation, i.e., $12000 \text{ kg}$.

Evaluation. 3 points for the number of large bags before the theft; 3 points for the weight of the remaining cement.