In a class test, the sum of the marks obtained by P in Mathematics and Science is 28. Had he got 3 marks more in Mathematics and 4 marks less in Science, the product of his marks, would have been 180. Find his marks in the two subjects.

Given:

In a class test, the sum of the marks obtained by P in Mathematics and Science is 28.

Had he got 3 marks more in Mathematics and 4 marks less in Science, the product of his marks, would have been 180.

To do:

We have to find his marks in the two subjects.

Solution:

Let the marks obtained by P in Mathematics be $x$.

This implies,

Marks obtained by him in Science $=28-x$.

New marks in Mathematics $=x+3$.

New marks in Science $=28-x-4=24-x$

According to the question,

$(x+3)\times(24-x)=180$

$x(24-x)+3(24-x)=180$

$24x-x^2+72-3x=180$

$21x-x^2=180-72$

$x^2-21x+108=0$

Solving for $x$ by factorization method, we get,

$x^2-12x-9x+108=0$

$x(x-12)-9(x-12)=0$

$(x-12)(x-9)=0$

$x-12=0$ or $x-9=0$

$x=12$ or $x=9$

If $x=12$, $28-x=28-12=16$

If $x=9$, $28-x=28-9=19$

Therefore, marks in Mathematics and Science are $12$ and $16$ or $9$ and $19$ respectively.

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Updated on: 10-Oct-2022

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