Question 4 (iii) - Cross Multiplication Method - Chapter 3 Class 10 Pair of Linear Equations in Two Variables

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Question4 Form the pair of linear equations in the following problems and find their solutions (if they exist) by any algebraic method : (iii) Yash scored 40 marks in a test, getting 3 marks for each right answer and losing 1 mark for each wrong answer. Had 4 marks been awarded for each correct answer and 2 marks been deducted for each incorrect answer, then Yash would have scored 50 marks. How many questions were there in the test? Let Number of Right answers be x & Number of Wrong answers be y Given that , Yash scored 40 marks if we get 3 marks for right answer and lose 1 mark for wrong answer 3x – y = 40 Also, Yash scored 50 marks if he gets 4 marks for correct answer and loses 2 mark for wrong answer 4x – 2y = 50 2(2x – y)= 50 (2x – y) = 50/2 2x – y = 25 Hence, our equations are 3x – y = 40 …(1) 2x – y = 25 …(2) From (1) 3x – y = 40 3x – 40 = y y = 3x – 40 Putting value of y in (2) 2x – y = 25 2x – (3x – 40) = 25 2x – 3x + 40 = 25 2x – 3x = 25 – 40 −x = −15 x = 15 Putting x in (1) 3x – y = 40 3(15) – y = 40 3(15) – y = 40 45 – y = 40 45 – 40 = y 5 = y y = 5 Therefore x = 15, y = 5 is the solution So, Number of right answers = x = 15 Number of wrong answers = y = 5 Total questions in the test = x + y = 15 + 5 = 20