Question : Vikas gave 3 examinations. The ratio of marks he scored in the 3 examinations is 3 : 5 : 6. The ratio of maximum marks of the 3 examinations is 7 : 11 : 10. If he scored 50 percent marks in total, how many examinations has he scored marks more than 50 percent?
Option 1: None
Option 2: 1
Option 3: 3
Option 4: 2
Correct Answer: 1
Solution :
If Vikas scored $3x, 5x, 6x$ marks out of $7y, 11y, 10y$ respectively.
Then, according to the question,
⇒ $3x+5x+6x = 0.5 × (7y+11y+10y)$
⇒ $14x=0.5×28y$
⇒ $x = y$
⇒ Percentage of Marks in first exam = $\frac{3x}{7y}$ × 100 = $\frac{3x}{7x}$ × 100 = 42.86%
⇒ Percentage of Marks in second exam = $\frac{5x}{11y}$ × 100 = $\frac{5x}{11x}$ × 100 = 45.45%
⇒ Percentage of Marks in third exam = $\frac{6x}{10y}$ × 100 = $\frac{6x}{10x}$ × 100 = 60%
So, he scored more than 50% marks in one subject only.
Hence, the correct answer is 1.
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