## Task 5 - 230735

Roland is calculating a division problem. He notices:

The dividend is $60\%$ of the quotient, and the divisor is $75\%$ of the quotient.

Prove that Roland's observations allow the quotient of the division problem to be determined uniquely! State this quotient!


If $Q$ is the quotient, then according to Roland's findings, the dividend is $\frac{3}{5} Q$ and the divisor is $\frac{3}{4} Q$. The division problem thus reads

$$
\frac{3}{5} Q:\left(\frac{3}{4} Q\right)
$$

Its result is $\frac{3}{5} \cdot \frac{4}{3}=\frac{4}{5}$.

This proves that the quotient can be uniquely determined from Roland's findings. It is $\frac{4}{5}$.