Question

In a class test , the sum of marks in maths and science is 28 .had he got 4 less marks in maths and 3 more marks in science the product of his marks would have been 180 . find his marks in the two subjects .​

Answer 1

$\huge{\mathfrak{Solution:-}}$

Let the marks obtained in mathematics be 'x' then the marks obtained in science will be 28 - x.

According to question,

$\sf{(x+3)(28-x-4)=180}$

$\sf{\implies (x+3)(24-x)=180}$

$\sf{\implies 24x-x^{2}+72-3x=180}$

$\sf{\implies 21x-x^{2}-108=180}$

$\sf{\implies x^{2}-21x+108=0}$

$\sf{\implies x^{2}-12x-9x+108=0}$

$\sf{\implies x(x-12)-9(x-12)=0}$

$\sf{\implies x=9,12}$

The marks obtained is mathematics can be 12 or 9.

If he obtained 12 marks in mathematics then he obtained 28 - 12 = 16 marks in science.

If he obtained 9 marks in mathematics then he obtained 28 - 9 = 19 marks in science.