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In a class test, Raveena got a total of 30 marks in English and Mathematics. Had she got 2 more marks in mathematics and 3 marks less in English, then the product of her marks obtained would have been 210. Find the individual marks obtained in the two subjects.

Answers (1)

Given $\rightarrow$ Marks in maths and english are 30.

$\Rightarrow M+E=30\;\;\;\;\;\; -(i)$

Also $(M+2)(E-3)=210 \;\;\;\;\;\;\; -(ii)$

From (i) $\Rightarrow M=30-E$

Putting value of M in equation (ii) :

$\Rightarrow \left ( 30-E+2 \right )\left ( E-3 \right )=210$

$\Rightarrow \left ( 32-E \right )\left ( E-3 \right )=210$

Let marks in English be $x\Rightarrow E=x$

$\Rightarrow (32-x)(x-3)=210$

$\Rightarrow 32x-x^2+3x-3\times 32=210$

$\Rightarrow -x^2+35x-96-210=0$

$\Rightarrow -x^2+35x-306=0$

$\Rightarrow x^2-35x+306=0$ (Multiply by (-1))

$\Rightarrow x^2-(17+18)x+306=0\;\;\;\;\;\;\; \left ( \therefore 306=17\times 18 \right )$

$\Rightarrow x^2-17x-18x+306=0$

$\Rightarrow x(x-17)-18(x-17)=0$

$\Rightarrow (x-18)(x-17)=0$

$\Rightarrow x=17 \;\;\;or\;\;\; x=18$

$\Rightarrow \text{Marks in English}=x$

Hence $E=17\;\;\; or \;\;\; E=18$

Assuming $E=17,$

$M=30-17$ (From (i))

$M=13$

$E=17,M=13$

Assuming $E=18,$

$M=30-18$ (From (i))

$M=12$

$E=18,M=12$

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Safeer PP

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