A student who gets 30% of the marks in an exam fails by 50 marks. Another student who gets 320 marks fails by 30 marks. Find the maximum marks.a)3000b)1000c)900d)1100Correct answer is option 'B'. Can you explain this answer?

Question

Answer

Let m as maximum marks

Now, according to question

⇒ 0.3 m + 50=320 + 30

⇒0.3 m = 300

m = 1000 marks

Answer

Understanding the Problem
To find the maximum marks of the exam, we need to deduce the total marks based on the information provided about the two students.
Information Given
- Student 1: Achieves 30% of the total marks and fails by 50 marks.
- Student 2: Scores 320 marks and fails by 30 marks.
Setting Up Equations
1. Let the maximum marks be denoted by M.
2. For Student 1:
- Score = 30% of M = 0.3M
- Since Student 1 fails by 50 marks, the passing marks are:
- 0.3M + 50 = Passing Marks
3. For Student 2:
- Score = 320 marks
- Since Student 2 fails by 30 marks, the passing marks are:
- 320 + 30 = 350 = Passing Marks
Equating the Passing Marks
- From Student 1:
- Passing Marks = 0.3M + 50
- From Student 2:
- Passing Marks = 350
Setting these two expressions equal gives us:
0.3M + 50 = 350
Solving for M
1. Rearranging the equation:
- 0.3M = 350 - 50
- 0.3M = 300
2. Dividing both sides by 0.3:
- M = 300 / 0.3
- M = 1000
Conclusion
The maximum marks for the exam is 1000. Thus, the correct answer is option B.

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