Final answer:
Joseph was 30 years old when he gained power in Egypt under Pharaoh, during the second intermediate period of Egyptian history, around 1800 BCE. Biblical records support this age, with other suggested ages lacking historical or biblical evidence.
Step-by-step explanation:
The age of Joseph when he was given power by Pharaoh can be determined from biblical records. According to the Book of Genesis in the Bible, Joseph was 30 years old when he entered the service of Pharaoh, the king of Egypt (Genesis 41:46). This timeline corresponds to the period roughly around 1800 BCE, which belongs to the second intermediate period of ancient Egyptian history, c. 1640-1540 BCE. This period is after the Old Kingdom (c. 2649-2150 BCE) and before the New Kingdom (c. 1550-1070 BCE). The role of the pharaoh during this time was as the ruler of a vast and populous kingdom, and Joseph's rise to power would have made him an influential figure within this expansive political and social structure. Therefore, the correct answer is 30 years old, and other figures like 143 or 40 years old are not supported by the historical or biblical context.