Out of the three annual examinations, each with a total of 500 marks, a student secured average marks of 45% and 55% in the first and second annual examinations. To have an overall average of 60%, how many marks does the student need to secure in the third annual examination?

Total marks for three examinations = 3x 500 = 1500
Total required marks in three examinations = 60% of 1500
=( 3 x 500 x 60 ) / 100
= 900
Marks secured in first examination = 45 % of 500
=( 500 x 45 ) / 100
=225
Marks secured in third examination = 55 % of 500
=( 500 x 55 ) / 100
=275
Thus, the required marks in third examination
=900 - ( 225 + 275 )
=900 - 500
= 400