In a multiple choice type question paper, 5 marks are awarded for the correct answer and 2 marks are deducted for the wrong answer. A student answered all the questions and obtained 69 marks. If 4 marks were awarded for the correct answer and 1 mark was deducted for the wrong answer, then he would have obtained 84 marks. How many questions were there in the question paper?

Let correct answers = c, wrong answers = w. Total questions n = c + w. Scheme 1: 5c - 2w = 69. Scheme 2: 4c - w = 84. From scheme 2: w = 4c - 84. Substitute in scheme 1: 5c - 2(4c - 84) = 69 → 5c - 8c + 168 = 69 → -3c = -99 → c = 33. Then w = 4(33) - 84 = 132 - 84 = 48. Total n = 33 + 48 = 81. Hmm, that gives 81 (option b). Let me verify: 5(33) - 2(48) = 165 - 96 = 69 ✓. 4(33) - 1(48) = 132 - 48 = 84 ✓. So n = 81, answer is (b).