A scored 30% marks and failed by 15 marks. B scored 40% marks and obtained 35 marks more than those required to pass. The pass percentage is-

MCQ Explanation: Pass Percentage Calculation

The question asks us to determine the pass percentage given the following data:

• Candidate A secured 30% marks and failed by 15 marks.

• Candidate B secured 40% marks and passed by 35 marks.

The answer choices are:

• 33%

• 38%

• 43%

• 46%

Solution:

Let's define the total marks as x. We need to find the passing percentage and ultimately confirm the options.

Step-by-Step Reasoning:

Step 1: Formulate equations based on the given data.

From Candidate A's information:

Since A failed by 15 marks, the actual marks scored by A can be written as:

30% of x = Passing Marks - 15

...or written as an equation:

(0.30)x = Passing Marks - 15

From Candidate B's information:

Since B passed by 35 marks, the actual marks scored by B can be written as:

40% of x = Passing Marks + 35

...or written as an equation:

(0.40)x = Passing Marks + 35

Step 2: Solve these equations simultaneously to find the Passing Marks.

We now have two equations:

• Equation 1: (0.30)x = Passing Marks - 15

• Equation 2: (0.40)x = Passing Marks + 35

We can use these equations to eliminate the Passing Marks variable:

First, express Passing Marks from Equation 1:

Passing Marks = (0.30)x + 15

Similarly, express Passing Marks from Equation 2:

Passing Marks = (0.40)x - 35

Equating both expressions for Passing Marks, we get:

(0.30)x + 15 = (0.40)x - 35

Step 3: Solve for x.

Rearranging the equation to simplify:

15 + 35 = (0.40)x - (0.30)x

50 = 0.10x

x = 500

Step 4: Find the Passing Marks

Substituting x back into Equation 1:

Passing Marks = (0.30)(500) + 15 = 150 + 15 = 165

Step 5: Calculate the passing percentage:

Passing Percentage = (Passing Marks / Total Marks) * 100

Passing Percentage = (165 / 500) * 100 = 33%

Conclusion:

The pass percentage is 33%. Thus, the correct answer is:33%