x = 25 -y Substituting in equation (2) 50 (25 - y) + 100y = 2000
1250 - 50y + 100y = 2000 50y = 2000 - 1250 = 750
y = 75050 = 15 x = 25 - 15 = 10 Hence, Rubina received ten `50 notes and fifteen `100 notes. Solution through the elimination method: In the equations, coefficients of x are 1 and 50 respectively. So,
Equation (1) × 50 : 50x + 50y = 1250 Equation (2) × 1 : 50x + 100y = 2000 same sign, so subtract (-) (-) (-) -50y = -750 or y = 750-- = 15 50Substitute y in equation (1) x + 15 = 25x = 25 - 15 = 10
Hence Rubina received ten D50 notes and fifteen D100 rupee notes. Example-9. In a competitive exam, 3 marks are awarded for every correct answer and forevery wrong answer, 1 mark will be deducted. Madhu scored 40 marks in this exam. Had 4marks been awarded for each correct answer and 2 marks deducted for each incorrect answer,Madhu would have scored 50 marks. If Madhu has attempted all questions, how many questionswere there in the test? Solution : Let the number of correct answers be x and the number of wrong answers be y. When 3 marks are given for each correct answer and 1 mark deducted for each wronganswer, his score is 40 marks. So 3x - y = 40 (1) His score would have been 50 marks if 4 marks were given for each correct answer and 2marks deducted for each wrong answer. Thus, 4x - 2y = 50 (2)