KöMaL 2018 K571

The headmaster of a school issued a decree that the legs of students' trousers must not be shorter than one fifth of their height. In the investigation of Sam's trousers length, the ethical committee concluded that the legs of his trousers were shorter than allowed, by exactly $\frac{2}{7}$ of the allowed minimum length. In addition, they also established that a 3-cm increase of the length of his trousers legs would still make it 20% shorter than allowed. How tall is Sam?