Mark 10:46,47 -- one man (Bartimaeus) was healed
Matthew 20:29,30 -- two blind men healed
When we carefully compare the records about these healings in Mark 10 and Matthew 20 we will again have a total picture which is free of any contradictions. The key to solving the apparent contradiction in this case is that we recognize how the records compliment rather than contradict each other.
Mark 10:46 puts the healing of blind Bartimaeus on a time "when they left [as they were just leaving]" Jericho; Matthew 20:29 happened as "they had left [having left]" Jericho and seemingly were already on the way. From the use of the participle form in the Greek texts in Mat 20:29 it can be concluded that the healing of the two blind men took place as Jesus and the crowd had already left Jericho behind whereas Bartimaeus had been sitting right at the exit of the citty of Jericho. There are several other points in which these two records differ; for example, there are not only differences in number of people and time of the healings, but also differences in their behaviour (Bartimaeus was begging, the other two were not); in what they cried when Jesus passed by; in what Jesus did in response (he had Bartimaeaus called to come, but the other two he himself called to come to him); in what they desired from Jesus (Bartimaeus wanted "that I might receive my sight", the other two wanted "that our eyes may be opened"); in what Jesus answered them and did (with Bartimaeus he said, "Go thy way; thy faith hath made thee whole", with the other two he touched their eyes and said nothing).
It is quite remarkable in this study to realize that shortly before these events another blind man had been healed near Jericho, i.e. when Jesus "was come nigh unto Jericho" (cp. Luke 18:35 - 19,1).
When we take the records in these three gospels we arrive at the following situation: Jesus was on his way to Jerusalem, and as he came nigh unto Jericho he met the first blind man whom he then healed. Then he went into Jericho with his disciples and passed through the ciry and when they were leaving Jericho he met the blind beggar Bartimaeaus at the exit of the city. He healed him when he shortly afterwards in the way met two more blind men he showed mercy on them as well and healed them. Thus, within a short period of time and all near Jericho four blind men were healed by Jesus. It was not that uncommon in biblical times and in the Bible lands to meet such a number of blind people in one city, also these people were not the only blind people whose healing by Jesus is recorded in the Bible.
What a great and marvellous saviour we have! He did not become tired after the healing of the first or second blind man within a short period of time, but he also showed mercy to the other two blind men and received them and healed them immediately.