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
• B. Her marks in mathematics and science are 14 and 16
• C. Her marks in mathematics and science are 12 and 18
• D. Her marks in mathematics and science are 11 and 19

Answer 1

Answer: (A), (C)

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

$(x+2)(27–x)=210$

$27x–x^2+54–2x=210$

$x^2–25x+156=0$

Applying quadratic formula to above equation, we get

$x=\frac{25\pm 1}{2}$

$x$ = 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).