Question

# The sum of Arushi’s marks in Mathematics and Science is 30. Had she got 2 marks more in Mathematics and 3 marks less in English, the product of their marks would have been 210. Choose the correct options on the basis of this information.

A

Her marks in mathematics and science are 13 and 17

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B

Her marks in mathematics and science are 14 and 16

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C

Her marks in mathematics and science are 12 and 18

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D

Her marks in mathematics and science are 11 and 19

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Solution

## The correct options are A Her marks in mathematics and science are 13 and 17 C Her marks in mathematics and science are 12 and 18 Let Arushi’s marks in Mathematics = x Then, her marks in Science = 30–x Her marks, if she had got 2 marks more in Mathematics = x+2 Her marks if she had got 3 marks less in English = 27–x Given condition is (x+2)(27–x)=210 27x–x2+54–2x=210 x2–25x+156=0 Applying quadratic formula to above equation, we get x=25±12 x = 13 and 12 Putting x = 13 and 12 in 30–x, we get 17 and 18 respectively. Therefore Arushi's marks in Mathematics and English are either (13, 17) or (12, 18).

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