He has held this position of Imam , under the title of Aga Khan IV , since July 11 , 1957 , when , at the age of 20 , he succeeded his grandfather , Sir Sultan Muhammad Shah Aga Khan III .
He has held this position under the title of Aga Khan since 11 July 1957 , when , at the age of 20 , he succeeded his grandfather , Sir Sultan Mahomed Shah Aga Khan .