Q42 of 168 Page 7

In a class test, the sum of Gagan marks in Mathematics and English is 45. If he had 1 more mark in Mathematics and 1 less in English, the product of marks would have been 500. Find the original marks obtained by Gagan in Mathematics and English separately.

Let the marks in maths be ‘X’ and English be ‘Y’.


X + Y = 45 equation 1


X = 45 – Y


(X + 1)(Y – 1) = 500


(45 – Y – 1)(Y – 1) = 500


Y2 – 43Y + 456 = 0


By solving this quadratic equation


Y2 – 24Y – 19Y + 456 = 0


Y(Y – 24) – 19(Y – 24) = 0


we get two values of Y


Y1 = 24


Y2 = 19


substitute both this values in equation 1


X1 + 24 = 45


X1 = 45 – 24


= 21


X2 + 19 = 45


X2 = 45 – 19


= 26


the marks in maths is 21, then marks in English is 24 and if the marks in maths is 26, then marks in English is 19.


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