Does the answering of one of two prayers, which were prayed at the same time, mean the answering of the second prayer?

There is no evidence that the acceptance of one prayer out of two simultaneously necessitates the acceptance of the other. Rather, the evidence indicates the contrary, as in the Hadith of the Prophet, peace and blessings be upon him, who asked his Lord for three things, and He granted him two and withheld one. The acceptance of a supplication does not necessarily mean granting the supplicant exactly what he asked for. Rather, it can be one of three things: the prayer is answered promptly, or it is stored for the Hereafter, or an equivalent evil is averted. The answer might be the attainment of the exact request at its time, or its delay for a wisdom, or the دفع of evil in its place, or its preservation for the Day of Judgment.