DIRECTIONS: Choose the most appropriate answer:Q. 'A' scored 30% marks and failed by 15 marks. 'B' scored 40% marks and obtained 35 marks more than those required to pass what is the pass percentage ?a)33%b)40%c)34%d)48%Correct answer is option 'A'. Can you explain this answer?

Question

Answer

Given Information:
- Student A scored 30% marks and failed by 15 marks.
- Student B scored 40% marks and obtained 35 marks more than those required to pass.

To Find:
The pass percentage.

Solution:
Step 1: Finding the Marks Obtained by Student A
Let the maximum marks be M.
According to the given information, Student A scored 30% marks and failed by 15 marks.
So, the marks obtained by Student A can be calculated as:
Marks obtained by Student A = 30% of M
Failed marks = 15

Therefore, we can write the equation as:
(Marks obtained by Student A) - (Failed marks) = (30/100) * M
(Marks obtained by Student A) - 15 = (30/100) * M
(Marks obtained by Student A) = (30/100) * M + 15

Step 2: Finding the Marks Obtained by Student B
According to the given information, Student B scored 40% marks and obtained 35 marks more than those required to pass.
So, the marks obtained by Student B can be calculated as:
Marks obtained by Student B = (Passing marks) + 35
Passing marks = (Pass percentage/100) * M

Therefore, we can write the equation as:
Marks obtained by Student B = (Pass percentage/100) * M + 35

Step 3: Finding the Pass Percentage
Since Student A failed, the passing marks for Student A would be equal to the marks obtained by Student A.
So, we can write:
(Pass percentage/100) * M = (30/100) * M + 15

Simplifying the equation, we get:
(Pass percentage/100) * M - (30/100) * M = 15
(Pass percentage - 30)/100 * M = 15
(Pass percentage - 30) = 15 * 100/M
Pass percentage - 30 = 1500/M
Pass percentage = 30 + 1500/M

We also know that the marks obtained by Student B is equal to the passing marks plus 35.
So, we can write:
(Pass percentage/100) * M + 35 = (40/100) * M

Simplifying the equation, we get:
(Pass percentage/100) * M - (40/100) * M = -35
(Pass percentage - 40)/100 * M = -35
(Pass percentage - 40) = -35 * 100/M
Pass percentage - 40 = -3500/M
Pass percentage = 40 - 3500/M

Step 4: Comparing the Two Equations
Since both equations represent the same pass percentage, we can equate the two equations and solve for M.

30 + 1500/M = 40 - 3500/M
1500/M + 3500/M = 40 - 30
(1500 + 3500)/M = 10
5000/M = 10
M = 5000/10
M = 500

Step 5: Finding the Pass Percentage
Substituting the value of M in any of

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