In a class test, the sum of Kamal's marks in Mathematics and English i

1.	In a class test, the sum of Kamal's marks in Mathematics and English is 40. Had he got 3 marks more in Mathematics and 4 marks less in English, the product of his marks would have been 360. Find his marks in two subjects separately.
Answer» Let the marks scored in maths be ‘X’. Marks in English is ‘(40–X)’. As, per the question, If he got 3 marks in maths & 4 marks less in English, Marks in Maths =X+3 Marks in English = 40–X–4 = 36–X Product = 360 (36 – X)(X + 3) = 360 (36X + 108 – X² – 3X) = 360 (33X + 108 – X²) = 360 X² – 33X + 360 – 108 = 0 X² – 33X + 252 = 0 X² – 21X – 12X + 252 = 0 X(X – 21) – 12(X – 21) = 0 (X– 12)(X – 21) = 0 X = 12 or 21 ∴ If marks in Maths = 12 then marks in English = 40 – 12 = 28 If marks in Maths = 21 then marks in English = 40 – 21 = 19

In a class test, the sum of Kamal's marks in Mathematics and English is 40. Had he got 3 marks more in Mathematics and 4 marks less in English, the product of his marks would have been 360. Find his marks in two subjects separately.

Answer»

Let the marks scored in maths be ‘X’.

Marks in English is ‘(40–X)’.

As, per the question,

If he got 3 marks in maths & 4 marks less in English,

Marks in Maths =X+3

Marks in English = 40–X–4 = 36–X

Product = 360

(36 – X)(X + 3) = 360

(36X + 108 – X² – 3X) = 360

(33X + 108 – X²) = 360

X² – 33X + 360 – 108 = 0

X² – 33X + 252 = 0

X² – 21X – 12X + 252 = 0

X(X – 21) – 12(X – 21) = 0

(X– 12)(X – 21) = 0

X = 12 or 21

∴ If marks in Maths = 12 then marks in English = 40 – 12 = 28

If marks in Maths = 21 then marks in English = 40 – 21 = 19