In a class test, the sum of Shefali's marks in Mathematics and English is 30. Had she got 2 marks more in Mathematics and 3 marks less in English, the product of her marks would have been 210. Find her marks in two subjects.

Given:

In a class test, the sum of Shefali's marks in Mathematics and English is 30.

Had she got 2 marks more in Mathematics and 3 marks less in English, the product of her marks would have been 210.

To do:

We have to find her marks in the two subjects.

Solution:

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

This implies,

Marks obtained by Shefali in English $=30-x$.

New marks in Mathematics $=x+2$.

New marks in English $=30-x-3=27-x$

According to the question,

$(x+2)\times(27-x)=210$

$x(27-x)+2(27-x)=210$

$27x-x^2+54-2x=210$

$25x-x^2=210-54$

$x^2-25x+156=0$

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

$x^2-12x-13x+156=0$

$x(x-12)-13(x-12)=0$

$(x-12)(x-13)=0$

$x-12=0$ or $x-13=0$

$x=12$ or $x=13$

If $x=12$, $30-x=30-12=18$

If $x=13$, $30-x=30-13=17$

Therefore, marks in Mathematics and English are $12$ and $18$ or $13$ and $17$ respectively.

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Updated on: 10-Oct-2022

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