Question

In a competitive exam , 3 marks are awarded for every correct answer and for every wrong answer
1 mark will be deducted.Madhu scored 40 marks in this exam. Had 4 marks been awarded for each
correct answer and 2 marks deducted for each wrong answer, Madhu would have scored 50 marks.
If madhu has attempted all questions, how many questions were there in the test.

Answer 1

Step-by-step explanation:

Given In a competitive exam , 3 marks are awarded for every correct answer and for every wrong answer 1 mark will be deducted. Madhu scored 40 marks i n this exam. Had 4 marks been awarded for each  correct answer and 2 marks deducted for each wrong answer, Madhu would have scored 50 marks.  If Madhu has attempted all questions, how many questions were there in the test.

• Let the number of correct answer be c and let the number of wrong answers be w
• According to the question 3 marks are awarded for every correct answer and 1 mark is deducted for every wrong answer. So we can write the equation as  
• 3c – w = 40 ------------1
• If 4 marks was awarded for each correct answer and 2 marks deducted for each wrong answer his score would have been 50 marks. So we can write the equation as  
• 4c – 2w = 50 -----------2
• Now we have the equations  
• 3c – w = 40
• 4c – 2w = 50
• Multiply the first equation by 2 we get
• 6c – 2w = 80
• 4c – 2w = 50
• On subtracting we get
• 2c = 30
• Or c = 15
• Now substituting c we get
• 3(15) – w = 40
• 45 – w = 40
• Or – w = - 5
• Or w = 5
• Therefore total number of questions in the test will be c + w = 15 + 5
•                = 20

Reference link will be

https://brainly.in/question/5483544