Can I go from Wutaishan city (submit) to Pingyao old city within the same day ?

Yes, it is possible!
1. There is one direct train between - K603! It leaves Wutaishan around 23:30 to get to Pingyao in around 5.5h! Or you can take a bus to Taiyuan first and then transfer to another bus to Pingyao!
2. By bus, the duration from Wutaishan to Taiyuan is around 4h and from Taiyuan to Pingyao old city, it takes around 1.5h!

Thanks for the reply.