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.

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Solution

The correct options are

**A**

**C**

Her marks in mathematics and science are 13 and 17

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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