Question

5. In a class test, the sum of Shefali's marks in Mathematics and English is
2 marks more in Mathematics and 3 marks less in English, the producing
would have been 210. Find her marks in the two subjects.
​

Answer 1

SOLUTION :  

Let the marks in Maths be x.

Then, the marks in English will be 30 - x.

A.T.Q

(x + 2)(30 - x - 3) = 210

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

⇒ -x² + 25x + 54 = 210

⇒ x² - 25x + 156 = 0

⇒ x² - 12x - 13x + 156 = 0

[By middle term splitting]

⇒ x(x - 12) -13(x - 12) = 0

⇒ (x - 12) (x - 13) = 0

⇒ (x - 12) = 0 or  (x - 13) = 0

⇒ x = 12  or x = 13

Case 1 :  

If the marks in Maths are 12, then marks in English will be 30 - 12 = 18

Case 2:  

If the marks in Maths are 13, then marks in English will be 30 - 13 = 17

Hence, the marks in Maths are (12,13) and marks in English are (18,17)

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Answer 2

• Let Shefali's marks in Mathematics = x
• Then, Shefali's marks in in English = 30-x

Now, according to the question,

• Marks in Mathematics = x+2
• Marks in English = (30-x-3) = 27-x

Given,

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

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

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

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

As,

• $D = \frac{- b± \sqrt{ {b}^{2} - 4ac } }{2a}$

$= \frac{25 ± \sqrt{ {( - 25)}^{2} - 4 \times 156 } }{2 \times 1}$

$= \frac{25 ± \sqrt{625 - 624} }{2}$

$= \frac{26}{2} \: \: \: \: and \: \: \: \: \frac{24}{2}$

$= 13 \: \: \: \: \:and \: \: \: \:12$

So,

Case 1

When the marks in Mathematics is 12.

Then, in English will be 30-12=18.

Case 2

When the marks in Mathematics is 13.

Then, in English will be 30-13=17.