10. A cell phone with a completely drained battery needs to be charged for 2 hours to fully recharge if it is not used in the meantime. If, however, it is used during charging, half of the introduced energy is immediately consumed, and only the remaining part accumulates in the battery. Knowing that it took 2 and a half hours to recharge the battery from zero, determine for how many minutes the phone was used during the charging process (assuming that, whether the phone is used or not, the energy stored over a period of time is proportional to its duration).
(A) 75
(B) 60
(C) 54
(D) 70
(E) 72
(10) The correct answer is $(B)$.

Let $E$ be the total energy that can be stored in the mobile phone. The energy stored in one minute without using it will be equal to $\frac{E}{120}$: the energy stored in one minute of usage will be equal to $\frac{1}{2} \cdot \frac{E}{120}=\frac{E}{240}$. If the time required for charging with $x$ minutes of usage is 150 minutes, then it must be that $(150-x) \frac{E}{120} + x \frac{E}{240} = E$, hence $x=60$.

Question proposed by Giorgio Navone.