In one of the books, that it read regularly in the mosques, it is written, without any supporting evidence, "that the person who memorizes the Holy Qur'aan will intercede for ten of his family members on the Day of Resurrection, all of whom deserved to enter Hell."
The above contradicts the Holy Qur'aan 31:33. Could you please clarify and let me have your answer with supporting evidence from the Holy Qur'aan and the Sunnah.

All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad is His slave and Messenger. We ask Allaah to exalt his mention as well as that of his family and all his companions.

The narration that the questioner pointed to is not an authentic one. It is reported by At-Tabaraani on the authority of Jaabir that the Prophet said: ''If a person who memorizes the Qur'aan, adheres to that which is permissible, and refrains from that which is forbidden, he will intercede for ten people of his family, all of whom deserved the fire.''  This narration is not authentic, and thus is not confirmed about the Prophet .

We draw the attention of the questioner, however, that there is no contradiction between the saying of Allaah (interpretation of the meaning): {O mankind! Be afraid of your Lord (by keeping your duty to Him and avoiding all evil), and fear a Day when no father can avail aught for his son, nor a son avail aught for his father.}[31:33], and the possibility of intercession by the believers on the Day of Judgment for their families. The Prophet said: ''The martyr will intercede for 70 people from his family''. [Abu Daawood and others]

Al-Qurtubi interpreted the above verse [31:33] saying: 'The meaning of this verse is that a father cannot bear the sin of his son, and the son cannot bear the sin of his father, and one of them will not be held accountable for the sins of the other one'.

Ibn Katheer said: 'This means that if the father wants to ransom himself from the punishment of that day by his son, this will not be accepted by him. And if the son wants to ransom himself from the punishment of that day by his father, this will not be accepted from him as well'.

But if one intercedes for the other and Allaah accepts that, then the person who is interceded for, will benefit. Allaah says (interpretation of the meaning): {And they cannot intercede except for him with whom He is pleased}[21:28]. Allaah also says (interpretation of the meaning): {On that day no intercession shall avail, except the one for whom the Most Gracious (Allaah) has given permission and whose word is accepted to Him}[20:109].

To conclude, there is no contradiction between the confirmed intercession and the verse stated by the questioner [31:33]. 

Allaah knows best.