In an exam every question correctly answered fetches 2 marks. Every question wrongly answered loses 1 marks. unanswered question have no marks associated with them. ram and shyam wrote this exam. ram attempted a certain number of questions and 30 % of them went wrong. shayam attempted a certain number of questions anf 40% of them went wrong. ram got 40 marks more than the pass mark. shyam got 25 marks more than the pass mark. the two of them together attempted a total of 100 questions.
so, what is the pass mark?
To solve this problem, let's break it down step by step:
1. Let's assume that Ram attempted x number of questions. We know that 30% of these went wrong, which means that 0.3x questions are wrong. Therefore, Ram answered (x - 0.3x) = 0.7x questions correctly.
2. Since every question correctly answered fetches 2 marks, Ram's total marks can be calculated as 2 * 0.7x = 1.4x.
3. We are given that Ram got 40 marks more than the pass mark. Let's assume the pass mark is y. So, Ram's total marks would be y + 40.
4. Equating the two expressions for Ram's marks, we get 1.4x = y + 40.
5. Similarly, let's assume that Shyam attempted y number of questions. We know that 40% of these went wrong, which means that 0.4y questions are wrong. Therefore, Shyam answered (y - 0.4y) = 0.6y questions correctly.
6. Shyam's total marks can be calculated as 2 * 0.6y = 1.2y.
7. We are given that Shyam got 25 marks more than the pass mark. So, Shyam's total marks would be y + 25.
8. Equating the two expressions for Shyam's marks, we get 1.2y = y + 25.
9. The problem states that the two of them together attempted a total of 100 questions. So, we have the equation x + y = 100.
Now, we have a system of equations:
1.4x = y + 40
1.2y = y + 25
x + y = 100
Solving these equations will give us the values of x and y, which represent the number of questions attempted by Ram and Shyam respectively.