Question

In a class test, the sum of Gagan's marks in maths and english is 45. If he had 1 more mark in Maths and 1 less in english, the product of marks would been 500. Find the original marks obtained by Gagan in maths and english seperately.



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Answer 1

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Answer 2

Answer: Marks in maths = 24 and English = 21,

Or marks in Maths = 19 and English = 26

Step-by-step explanation:

Let x be the marks in Maths and y be the marks in English,

x + y = 45 ⇒ y = 45 - x,

Also, If he had 1 more mark in Maths and 1 less in English, the product of marks would been 500.

(x+1)(y-1) = 500

⇒ (x+1)(45-x-1)=500 ⇒ (x+1)(44-x) = 500

⇒ 44x + 44 - x² - x = 500

⇒ 43x - x²-456=0

⇒ x²-43x + 456 = 0

⇒ x²- 24x - 19x + 456 = 0

⇒ x(x-24) - 19(x-24) =0

⇒ (x-24)(x-19) = 0

If x -24 = 0⇒ x = 24, ⇒ y = 45 - 24 = 21

If x - 19 = 0⇒ x = 19, ⇒ y = 45 - 19 = 26,

Hence, the original marks in Maths = 24 and in English = 21,

Or the original marks in Maths = 19 and in English = 26