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In a class test, the sum of Anamika's marks obtained in Maths and Science is 30. Had she got 2 marks more in Maths and 3 marks less in Science, the product of the marks would have been 210. Find the marks she got in the two subjects.
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Let the marks obtained in Maths be $x$
Then the marks obtained in Science = $30 - x$
$(x + 2)(30 - x - 3) = 210$ (2 Marks)
$\Rightarrow x^2 - 25x + 156 = 0$ (1 Mark)
$\Rightarrow (x-13)(x - 12) = 0$ (1/2 Mark)
$\therefore x = 13, x = 12$ (1/2 Mark)
Either marks in Maths and Science are 13 and 17 respectively (1/2 Mark)
or marks in Maths and Science are 12 and 18 respectively (1/2 Mark)
Then the marks obtained in Science = $30 - x$
$(x + 2)(30 - x - 3) = 210$ (2 Marks)
$\Rightarrow x^2 - 25x + 156 = 0$ (1 Mark)
$\Rightarrow (x-13)(x - 12) = 0$ (1/2 Mark)
$\therefore x = 13, x = 12$ (1/2 Mark)
Either marks in Maths and Science are 13 and 17 respectively (1/2 Mark)
or marks in Maths and Science are 12 and 18 respectively (1/2 Mark)