Madhu obtains 32% of the maximum marks in a bank examination and fails by 8 marks. Kumar, who appears for the same examination, secures 42% of the total marks and scores 16 marks more than the cut off. What are the cut off marks in the examination?

Introduction / Context:
This question combines percentage marks and pass or cut off marks. It checks how well you convert percentages into actual scores using the same total marks and then use the information to determine the cut off.

Given Data / Assumptions:

• Let the maximum marks in the exam be M.• Madhu scores 32% of M and fails by 8 marks.• Kumar scores 42% of M and gets 16 marks more than the cut off.• The cut off is the minimum marks needed to pass.• We must find the value of the cut off in marks.

Concept / Approach:
Let C be the cut off. Madhu has C − 8 marks, and this equals 32% of M. Kumar has C + 16 marks, and this equals 42% of M. We can form two equations in M and C, subtract one from the other to eliminate C and solve for M, then substitute back to find C.

Step-by-Step Solution:
Step 1: Madhu score equation: 0.32M = C − 8.Step 2: Kumar score equation: 0.42M = C + 16.Step 3: Subtract the first equation from the second.Step 4: Left side: 0.42M − 0.32M = 0.10M.Step 5: Right side: (C + 16) − (C − 8) = 24.Step 6: So 0.10M = 24, hence M = 24 / 0.10 = 240.Step 7: Substitute M into Madhu equation: 0.32 * 240 = C − 8.Step 8: Compute 0.32 * 240 = 76.8, so C − 8 = 76.8.Step 9: Therefore C = 76.8 + 8 = 84.8.

Verification / Alternative check:
Check with Kumar. Forty two percent of 240 is 100.8. The difference between Kumar marks and cut off is 100.8 − 84.8 = 16, which matches the question data, so the cut off value is correct.

Why Other Options Are Wrong:
Values 76.8 and 78.8 do not satisfy both student conditions at the same time when substituted back. The option 86.8 also fails the required difference relationships.

Common Pitfalls:
A common mistake is to treat the percentages as if they were directly the cut off instead of solving the simultaneous equations. Mixing up who failed by 8 and who got 16 more than the cut off also leads to wrong equations.

Final Answer:
The cut off marks in the examination are 84.8.