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 ?a)450b)400c)350d)300e)None of the AboveCorrect answer is option 'B'. Can you explain this answer?

Question

Answer

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

Answer

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

Answer

Solution:

Let the marks secured by the student in the third annual examination be x.

Total marks secured by the student in three annual examinations = (45% of 500) + (55% of 500) + x

= 0.45 × 500 + 0.55 × 500 + x

= 225 + 275 + x

= 500 + x

According to the question, the overall average of the student should be 60%.

Therefore, (Total marks secured by the student in three annual examinations) / (Total marks for all three annual examinations) × 100 = 60%

=> [(500 + x) / (500 × 3)] × 100 = 60%

=> (500 + x) / 1500 = 0.6

=> 500 + x = 0.6 × 1500

=> 500 + x = 900

=> x = 900 - 500

=> x = 400

Hence, the student needs to secure 400 marks in the third annual examination to have an overall average of 60%. Therefore, the correct answer is option (B).

Similar Quant Doubts

60% of the students of a class are boys and in an examination, 80% of the girls scored more than 40 marks (out of a maximum possible 150 marks). If 60% of the total students scored more than 40 marks in the same examination, find the fraction of the boys who scored 40 marks or less.

The average marks obtained by 100 candidates in an examination are 45. If the average marks of the passed students are 50 while the average marks of the failed students is 40. Then find the number of students who passed the examination.

Top Courses for Quant

Related Content

Quant Courses

Related Exams

Related Question Answers

Related Searches

Company