एक वस्तुनिष्ठ प्रकार के प्रश्न-पत्र में, सही उत्तर के लिए 5 अंक दिए जाते हैं और गलत उत्तर के लिए 2 अंक घटा दिए जाते हैं। एक विद्यार्थी ने सभी प्रश्नों के उत्तर दिए और उसे 69 अंक मिले। यदि उसे एक सही उत्तर के लिए 4 अंक दिए जाते और एक गलत उत्तर के लिए 1 अंक घटा दिया जाता, तो उसे 84 अंक मिलते। प्रश्न-पत्र में कितने प्रश्न थे?
सही उत्तर: (b) 81
मान लीजिए कुल प्रश्नों की संख्या n है, जिसमें से सही उत्तर c और गलत उत्तर w हैं (c + w = n)। स्थिति 1: 5c - 2w = 69। स्थिति 2: 4c - w = 84। समीकरण 2 से, w = 4c - 84। इसे समीकरण 1 में रखने पर: 5c - 2(4c - 84) = 69 => 5c - 8c + 168 = 69 => -3c = -99 => c = 33। अब w = 4(33) - 84 = 48। कुल प्रश्न n = c + w = 33 + 48 = 81। अतः विकल्प (b) सही है।
In English (Question & Model Answer)
In an objective type question paper, 5 marks are awarded for a correct answer and 2 marks are deducted for a wrong answer. A student attempted all the questions and got a score of 69. Had he been awarded 4 marks for a correct answer and 1 mark deducted for a wrong answer, he would have scored 84. How many questions were there in the question paper?
Correct Option: (b) 81
Let the total number of questions be n. Since the student attempted all questions, let the number of correct answers be c and wrong answers be w, so c + w = n. Case 1: 5 marks for correct, 2 deducted for wrong, total score = 69. Equation 1: 5c - 2w = 69. Case 2: 4 marks for correct, 1 deducted for wrong, total score = 84. Equation 2: 4c - 1w = 84. From Equation 2, w = 4c - 84. Substitute w into Equation 1: 5c - 2(4c - 84) = 69 => 5c - 8c + 168 = 69 => -3c = 69 - 168 => -3c = -99 => c = 33. Now find w: w = 4(33) - 84 = 132 - 84 = 48. Total questions n = c + w = 33 + 48 = 81. Hence, the total number of questions in the paper was 81. Option (b) is correct.