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Rohini had scored 10 more marks in her mathematics test out of 30 marks, 9 times these marks would have been the square of her actual marks. How many marks did she get in the test?
- a)14
- b)16
- c)15
- d)18
Correct answer is option 'C'. Can you explain this answer?
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Rohini had scored 10 more marks in her mathematics test out of 30 mar...
Let her actual marks be x
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Therefore,
9 (x + 10) = x2
⇒ x2 – 9x – 90 = 0
⇒ x2 – 15x + 6x – 90 = 0
⇒ x(x – 15) + 6 (x – 15) = 0
⇒ (x + 6) (x – 15) = 0
Therefore x = – 6 or x =15
Since x is the marks obtained, x ≠ – 6.
Therefore, x = 15.
Most Upvoted Answer
Rohini had scored 10 more marks in her mathematics test out of 30 mar...
Given: Rohini had scored 10 more marks in her mathematics test out of 30 marks, 9 times these marks would have been the square of her actual marks.
Let's assume that Rohini scored x marks in the test.
According to the question, if Rohini had scored 10 more marks, she would have scored x+10 marks.
Also, given that 9 times these marks (x+10) would have been the square of her actual marks (x).
Therefore, we can write the equation as:
9(x+10) = x^2
Expanding the equation, we get:
9x + 90 = x^2
Bringing all the terms to one side, we get:
x^2 - 9x - 90 = 0
Factorizing the equation, we get:
(x-15)(x+6) = 0
Therefore, x = 15 or x = -6.
Since the number of marks cannot be negative, we can conclude that Rohini scored 15 marks in the test.
Hence, the correct answer is option C, i.e., 15.
Let's assume that Rohini scored x marks in the test.
According to the question, if Rohini had scored 10 more marks, she would have scored x+10 marks.
Also, given that 9 times these marks (x+10) would have been the square of her actual marks (x).
Therefore, we can write the equation as:
9(x+10) = x^2
Expanding the equation, we get:
9x + 90 = x^2
Bringing all the terms to one side, we get:
x^2 - 9x - 90 = 0
Factorizing the equation, we get:
(x-15)(x+6) = 0
Therefore, x = 15 or x = -6.
Since the number of marks cannot be negative, we can conclude that Rohini scored 15 marks in the test.
Hence, the correct answer is option C, i.e., 15.
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Rohini had scored 10 more marks in her mathematics test out of 30 marks, 9 times these marks would have been the square of her actual marks. How many marks did she get in the test?a)14b)16c)15d)18Correct answer is option 'C'. Can you explain this answer?
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