If ratio of marks scored by a 5th student X in the written exam and practical exam is 5 3 and the we...........

Quantitative Aptitude (SBI-PO) Case Studies

Direction: Study the given information carefully and answer the following questions.
Four students i.e. A, B, C and D appeared for written and practical examinations of year 2019-20
The information given below is known:
Total Maximum Marks = Maximum marks of written Exam + Maximum marks of practical Exam
Total Maximum weighted score = Maximum marks in written exam × weighted % + Maximum marks in practical exam × weighted %
Weighted score = Marks obtained in written exam × weighted % + Marks obtained in practical exam × weighted %
Weighted percentage of written exam is 60% and that of practical exam is 40%.
Also, maximum marks of written exam is 80 and that of practical exam is 60
It is given that:
Total weighted score of A is 52 . Total weighted score of B is 52 and B obtained 55 marks in practical exam.
C obtained 50 marks in practical exam. Marks obtained by D in written examination is 70 and D obtained 75% marks in practical exam.

If ratio of marks scored by a 5th student X in the written exam and practical exam is 5 : 3 and the weighted score of X is 52.5, then what is the sum of the marks scored by X in written and practical exams?

100

None of these

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Explanation:

Let marks obtained by B in written exam = Y
Given, marks obtained by B in practical exam = 55, then
0.6 × Y + 0.4 × 55 = 52
⇒ 0.6Y + 22 = 52
⇒ Y = 50
Marks obtained by D in written exam = 70
Marks obtained by D in practical exam = 75% of 60 = 45
Total weighted score of D = 0.6 × 70 + 0.4 × 45 = 60

Let the marks scored by X in written and practical exams = 5a and 3a, then
Total weighted score of X = 0.6 × 5a + 0.4 × 3a
⇒ 52.5 = 3a + 1.2a = 4.2a
⇒ a = 52.5/4.2= 12.5
The sum of the marks scored by X in written and practical exams = 5a + 3a = 8a = 8 × 12.5 = 100
Hence, option 3 is correct.