How old does a star appear to us on Earth if it is actually 10 million years old and located 100 million light-years away?

The age a star appears to observers on Earth is based on its actual age and the time taken for its light to reach us. In this scenario, the star is 10 million years old, which means that it has existed for that length of time. The distance of 100 million light-years indicates how far away the star is, but it does not affect the actual age of the star itself.

When we observe the star, we are seeing the light that left the star 100 million years ago. However, despite the distance, the star's current age is still 10 million years. The light emitted by the star took 100 million years to reach us, but at the moment of observation, we are assessing the star's existence based on its inherent age of 10 million years. This intrinsic age remains constant regardless of its light travel time, reflecting the lifetime of the star from the point of its formation.

Therefore, the correct interpretation is that, based on its formation and the duration it has existed, the star appears to be 10 million years old to us on Earth.