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Marks & Exams

Introduction

In aptitude tests, many questions involve marks and exams. These problems are based on percentage of marks obtained, total marks, and passing marks.

Such questions are very practical because they reflect real exam scoring. By applying simple percentage formulas, we can solve them step by step.

Pattern: Marks & Exams

Pattern

The key idea: Marks obtained = (Percentage ÷ 100) × Total marks

To find pass marks, add/subtract the difference from the marks obtained as per the question.

Fail/Pass difference questions are solved by using total marks × (pass% ÷ 100).

Step-by-Step Example

Question

A student scores 40% of the total marks in an exam and fails by 20 marks. If the pass percentage is 50%, find the total marks of the exam.

Solution

  1. Step 1: Represent total marks with a variable

    Let total marks = M.

  2. Step 2: Calculate student's obtained marks

    Marks obtained = (40/100) × M = 0.4M

  3. Step 3: Calculate pass marks

    Pass marks = (50/100) × M = 0.5M

  4. Step 4: Apply failure condition

    Pass marks - Obtained marks = 20 → 0.5M - 0.4M = 20

  5. Step 5: Solve the equation

    0.1M = 20 → M = 20 ÷ 0.1 = 200

  6. Final Answer:

    200

  7. Quick Check:

    Student’s marks = 40% of 200 = 80
    Pass marks = 50% of 200 = 100
    Difference = 20 ✅

Quick Variations

Sometimes the question gives marks scored and pass marks, and asks for the percentage. Use: (Marks scored ÷ Total marks) × 100.

If the student passes by X marks, then (Marks scored - Pass marks = X).

Trick to Always Use

  • Step 1: Let total marks = M.
  • Step 2: Write student’s score using %.
  • Step 3: Write pass marks using %.
  • Step 4: Apply pass/fail condition.
  • Step 5: Solve and verify.

Summary

Summary

  • Use Marks = (Percentage ÷ 100) × Total marks.
  • Pass marks = (Pass% ÷ 100) × Total marks.
  • Fail condition → Pass marks - Obtained = difference.
  • Pass condition → Obtained - Pass marks = difference.

Example to remember:
Total marks = 200 when 40% fails by 20 marks and pass% = 50%

Practice

(1/5)
1. A student scores 180 marks out of 300. Find his percentage.
easy
A. 55%
B. 60%
C. 58%
D. 62%

Solution

  1. Step 1: Apply the percentage formula

    Percentage = (Obtained ÷ Total) × 100 → (180 ÷ 300) × 100.

  2. Step 2: Calculate the percentage

    180 ÷ 300 = 0.6 → 0.6 × 100 = 60%.

  3. Final Answer:

    60% → Option B

  4. Quick Check:

    10% of 300 = 30 → 6 × 30 = 180 ✅
Hint: Divide obtained by total, then multiply by 100.
Common Mistakes: Swapping numerator/denominator (using Total ÷ Obtained).
2. If pass marks are 40% of 200, what are the pass marks?
easy
A. 80
B. 70
C. 90
D. 100

Solution

  1. Step 1: Use the pass marks formula

    Pass marks = (Pass% ÷ 100) × Total → (40 ÷ 100) × 200.

  2. Step 2: Compute the value

    0.4 × 200 = 80.

  3. Final Answer:

    80 → Option A

  4. Quick Check:

    10% of 200 = 20 → 4 × 20 = 80 ✅
Hint: Convert percent to decimal (40% → 0.4) then multiply by total.
Common Mistakes: Using 40 instead of 0.4 in multiplication (gives 8, wrong scale).
3. A student scored 300 out of 500 and passed by 50 marks. Find the pass percentage.
medium
A. 45%
B. 48%
C. 50%
D. 52%

Solution

  1. Step 1: Determine pass marks using the margin

    Student scored 300 and passed by 50 → Pass marks = 300 - 50 = 250.

  2. Step 2: Convert pass marks to percentage

    Pass% = (Pass marks ÷ Total) × 100 = (250 ÷ 500) × 100 = 50%.

  3. Final Answer:

    50% → Option C

  4. Quick Check:

    250 is half of 500 → 50% ✅
Hint: Pass marks = obtained - margin; then (pass ÷ total) × 100.
Common Mistakes: Adding the margin instead of subtracting when interpreting 'passed by'.
4. A boy scored 35% of 400 marks. How many marks did he score?
medium
A. 140
B. 135
C. 130
D. 145

Solution

  1. Step 1: Apply the marks formula

    Marks = (Percent ÷ 100) × Total → (35 ÷ 100) × 400.

  2. Step 2: Compute marks obtained

    0.35 × 400 = 140.

  3. Final Answer:

    140 → Option A

  4. Quick Check:

    10% of 400 = 40 → 30% = 120, 5% = 20 → total = 140 ✅
Hint: Split 35% into 30% + 5% for mental math.
Common Mistakes: Multiplying by 35 instead of 0.35 (gives 14000).
5. A student secures 360 marks out of 600. If pass marks are 50%, find by how many marks he passed.
medium
A. 40
B. 50
C. 60
D. 70

Solution

  1. Step 1: Compute pass marks

    Pass marks = 50% of 600 = (50 ÷ 100) × 600 = 300.

  2. Step 2: Find how many marks above pass

    Difference = 360 - 300 = 60.

  3. Final Answer:

    60 → Option C

  4. Quick Check:

    360 is 60 more than 300 → passed by 60 marks ✅
Hint: Find pass threshold first, then subtract from obtained marks.
Common Mistakes: Calculating pass% incorrectly (e.g., using 60% instead of 50%).

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