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 their marks would have been 210. Find her marks in the two subjects ?

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Solution:

⇒ Let the marks in Math be x

∴ Marks in English = 30 - x

A/Q

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

$\large \Rightarrow 27x-x^{2}+54-2x= 210$

$\large \Rightarrow 25x-x^{2}+54= 210$

$\large \Rightarrow x^{2}-25x+210-54=0$

$\large \Rightarrow x^{2}-25x+156=0$

$\large \Rightarrow x^{2}-\left ( 12+13 \right )x+156=0$

$\large \Rightarrow x^{2}-12x-13x+156=0$

$\large \Rightarrow x\left ( x-12 \right )-13\left ( x-12 \right )=0$

$\large \Rightarrow \left ( x-12 \right )\left ( x-13 \right )=0$

$\large \Rightarrow x-12=0,\Rightarrow x-13=0$

$\large \Rightarrow x=12,\Rightarrow x=13$

∴ If Mark In Math is = 12

⇒ Then Mark in English is = 30 - 12 = 18

∴ If Mark In Math is = 13

⇒ Then Mark in English is = 30 - 13 = 17

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