Question
Download Solution PDFVikas gave 3 examinations. The respective ratio of marks scored by him in the 3 examinations is 3 ∶ 5 ∶ 4. The respective ratio of maximum marks of the 3 examination is 8 ∶ 7 ∶ 9. If he scored 50 percent marks in total, then in how many examination has he scored marks more than 50 percent?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
Vikas gave 3 examinations. The respective ratio of marks scored by him in the 3 examinations is 3 ∶ 5 ∶ 4.
The respective ratio of maximum marks of the 3 examinations is 8 ∶ 7 ∶ 9.
He scored 50 percent marks in total.
Formula used:
Total marks scored = 50% of total maximum marks
Calculations:
Let the marks scored in the three exams be 3x, 5x, and 4x respectively.
Let the maximum marks of the three exams be 8y, 7y, and 9y respectively.
Total marks scored = 3x + 5x + 4x = 12x
Total maximum marks = 8y + 7y + 9y = 24y
Total marks scored = 50% of total maximum marks
⇒ 12x = 50% of 24y
⇒ 12x = 0.5 × 24y
⇒ 12x = 12y
⇒ x = y
Marks scored in each examination:
Exam 1: 3x = 3y
Exam 2: 5x = 5y
Exam 3: 4x = 4y
Percentage marks in each examination:
Exam 1: (3y / 8y) × 100 = 37.5%
Exam 2: (5y / 7y) × 100 = 71.43%
Exam 3: (4y / 9y) × 100 = 44.44%
∴ The number of examinations in which he scored more than 50% is 1.
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