Mark 10:46-52:

And they came to Jericho: and as he went out of Jericho with his disciples and a great number of people, blind Bartimaeus, the son of Timaeus, sat by the highway side begging.
And when he had heard that it was Jesus of Nazareth, he began to cry out, and say, Jesus, thou Son of David, have mercy on me.
And many charged him that he should hold his peace: but he cried the more a great deal, thou Son of David, have mercy on me.
And Jesus stood still, and commanded him to be called.  And they call the blind man, saying unto him, Be of good comfort, rise; he calleth thee.
And he, casting away his garment, rose, and came to Jesus.
And Jesus answered and said unto him, What wilt thou that I should do unto thee? The blind man said unto him, Lord, that I may receive my sight.
And Jesus said to him, Go thy way; thy faith hath made thee whole.  And immediately he received his sight, and followed Jesus in the way.

Notes on Mark 10:46-52:

Mark only tells what happened to Bartimaeus; Matthew records that there were two blind men.  (Mark’s story doesn’t mean that there weren’t two; it just records what happened to Bartimaeus.)

Mark records that Jesus said, “Your faith has made you whole,” while Matthew omitted that part.

Mark also mentions a detail that Matthew omits – Bartimaeus cast away his garment when he came to Jesus.  It is POSSIBLE that his garment identified him as a beggar and/or a blind person and that this casting away of his garment was because Bartimaeus was totally convinced that after he encountered Jesus, he would be The Man Formerly Known as Blind Bartimaeus.  We don’t know this for sure because the Bible doesn’t explicitly say anything about his garment.  However, there is no other apparent explanation for why Bartimaeus would do it.  If he were just cold, he could have received from Jesus with his garment still on because he was in faith anyway.

Matthew mentions the fact that Jesus actually touched a blind man, while Mark omits this detail.

See also:

Matthew 20:30-34
Notes on Matthew 20:30-34
According to YOUR FAITH Be It Done unto You
How Much Do You Desire Healing?
What Every Elder is Commanded to Believe
Strange Ways to Get Healed
Condition: Blindness