Jasmin has a mobile phone that runs on a battery. When the battery is dead, it takes $2$ hours to recharge it fully, if she is not using the phone. If she uses the phone while recharging, $75\%$ of the charge obtained is immediately consumed and the remaining is stored in the battery. One day, her battery died. Jasmin took $2$ hours $30$ minutes to recharge the battery fully. For how many minutes did she use the phone while recharging?