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. What is the pass mark ?
Let's solve this question step-by-step:
1. Let's assume that Ram attempted "x" questions and Shyam attempted "y" questions.
2. According to the given information, Ram's 30% of attempted questions went wrong, which means that 70% of attempted questions were correct. So, Ram's number of correct answers is 0.7x.
3. Similarly, Shyam's number of correct answers is 0.6y because 40% of his attempted questions went wrong.
4. We know that each correct answer earns 2 marks, so Ram's total marks can be calculated by multiplying his number of correct answers by 2. Hence, his total marks for correct answers is 2 * 0.7x = 1.4x marks.
5. As per the given information, Ram got 40 marks more than the pass mark. So, we can express Ram's total marks as (Pass Mark + 40) marks.
6. Therefore, we can write the equation as follows: 1.4x = Pass Mark + 40.
7. In a similar manner, Shyam's total marks for correct answers can be calculated as 2 * 0.6y = 1.2y marks.
8. Shyam's total marks can be expressed as (Pass Mark + 25) marks. So, we can write the equation as follows: 1.2y = Pass Mark + 25.
9. The sum of the number of attempted questions by Ram and Shyam is given as 100, so we can write the equation as x + y = 100.
10. We now have 3 equations:
- 1.4x = Pass Mark + 40
- 1.2y = Pass Mark + 25
- x + y = 100
11. Let's solve these equations to find the pass mark for the exam.
To solve this problem, we need to break it down into smaller steps:
Step 1: Determine the number of questions attempted by Ram and Shyam.
Let's represent the number of questions attempted by Ram as 'r' and the number of questions attempted by Shyam as 's'. Since the total number of questions attempted by both of them is 100, we can write the equation: r + s = 100.
Step 2: Calculate the number of wrong answers by Ram and Shyam.
Given that 30% of Ram's attempted questions and 40% of Shyam's attempted questions went wrong, we can calculate the number of wrong answers:
Number of wrong answers by Ram = 0.30 * r
Number of wrong answers by Shyam = 0.40 * s
Step 3: Calculate the number of correct answers by Ram and Shyam.
Since every correctly answered question fetches 2 marks and every wrongly answered question loses 1 mark, we can calculate the number of correct answers:
Number of correct answers by Ram = r - (0.30 * r) = 0.70 * r
Number of correct answers by Shyam = s - (0.40 * s) = 0.60 * s
Step 4: Determine the marks obtained by Ram and Shyam.
Given that Ram got 40 marks more than the pass mark and Shyam got 25 marks more than the pass mark, we can write the equation:
Marks obtained by Ram - Marks obtained by Shyam = 40
Since every correct answer gives 2 marks, we can rewrite the equation using the number of correct answers:
2 * (Number of correct answers by Ram) - 2 * (Number of correct answers by Shyam) = 40
Substituting the values calculated in Step 3:
2 * (0.70 * r) - 2 * (0.60 * s) = 40
Step 5: Determine the pass mark.
The pass mark is the total marks obtained if every question is correctly answered (i.e., 2 marks per question).
Pass mark = 2 * Total number of questions
Substituting the total number of questions attempted by both Ram and Shyam:
Pass mark = 2 * 100
Now, we have all the equations needed to solve the problem. Let's solve them simultaneously to find the pass mark.
if the pass mark is p, then if Ram attempted x questions, then Shyam attempted (100-x) questions. So,
2(.7x)-1(.3x) = p+40
2(.6(100-x))-1(.4(100-x)) = p+25
now just solve for p.