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 thir

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Q: 136 (IAS/1998)
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 ?

question_subject: 

Maths

question_exam: 

IAS

stats: 

0,3,5,2,3,2,1

keywords: 

{'average marks': [0, 1, 0, 0], 'third annual examination': [0, 1, 0, 0], 'many marks': [0, 1, 0, 0], 'annual examinations': [0, 1, 0, 0], 'second annual examinations': [0, 1, 0, 0], 'overall average': [0, 1, 0, 0], 'marks': [0, 1, 3, 2]}

Let`s calculate the marks needed in the third annual examination to have an overall average of 60%.

We are given that there are three annual examinations, each with a total of 500 marks.

To calculate the overall average, we need to consider the weightage of each examination.

Let`s assume the marks obtained in the third annual examination as "x".

The total marks obtained in the first annual examination can be calculated as 45% of 500, which is 0.45 * 500 = 225.

The total marks obtained in the second annual examination can be calculated as 55% of 500, which is 0.55 * 500 = 275.

The total marks obtained in the third annual examination can be calculated as x.

Now, we can calculate the total marks obtained in all three examinations:

225 + 275 + x = total marks

The overall average is desired to be 60%. We can express this as a fraction of 60/100.

The overall average can be calculated using the formula:

(225 + 275 + x) / (3 * 500) = 60/100

Simplifying the equation:

(500 + x) / 1500 = 60/100

Cross-multiplying:

100(500 + x) = 60 * 1500

50000 + 100x = 90000

100x = 90000 - 50000

100x = 40000

x = 40000 / 100

x = 400

Therefore, the student needs to secure 400 marks in the third annual examination to have an overall average of 60%.

The closest option given is 400, which is the correct answer.