Question

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.​

Answer 1

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Let us say, the marks of Shefali in Maths be x.

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

As per the given question,

(x + 2)(30 – x – 3) = 210

(x + 2)(27 – x) = 210

⇒ -x^2 + 25x + 54 = 210

⇒ x^2 – 25x + 156 = 0

⇒ x^2 – 12x – 13x + 156 = 0

⇒ x(x – 12) -13(x – 12) = 0

⇒ (x – 12)(x – 13) = 0

⇒ x = 12, 13

Therefore,

if the marks in Maths are 12,

then marks in English will be 30 – 12 = 18 and

the marks in Maths are 13,

then marks in English will be 30 – 13 = 17.

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Answer 2

Answer:

• let maths marks=x,and english=y
• so ATQ(according to question),
• x+y=30(given)-------(1)
• (x+2)(y-3)=210--------(2)
• from(1)x=30-y---------(3) put into (2)
• (30-y+2)(y-3)=210
• (32-y)(y-3)=210
• 32y-96-y^2+3y=210
• y^2-35y+96=-210
• y^2-32y-3y+96=-210
• y(y-32)-3(y-32)=-210
• (y-3)(y-32)=-210
• y=-207,-188