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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)450
- b)400
- c)350
- d)300
- e)None of the Above
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
Out of the three annual examinations, each with a total of 500 marks, ...
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
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
Most Upvoted Answer
Out of the three annual examinations, each with a total of 500 marks, ...
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
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
Community Answer
Out of the three annual examinations, each with a total of 500 marks, ...
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).
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).
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