A boy appears for a test and scores 35% but fails by 10 marks. If he had scored 46%, he would have passed
by 12 marks. What is the pass mark?
(1) 70
(2) 74
(3) 80
(4) 86

📘 Problem Statement

A boy appears for a test and scores 35% but fails by 10 marks.
If he had scored 46%, he would have passed by 12 marks.
What is the pass mark?

Options:

1. 70

2. 74

3. 80

4. 86

🧮 Step-by-Step Solution

Let the total marks of the exam be x.
We’re told:

• 35% of x = pass marks – 10

• 46% of x = pass marks + 12

Let’s form equations:

Equation 1:

$$0.35x=P-10$$

Equation 2:

$$0.46x=P+12$$

Now subtract Equation 1 from Equation 2:

$$(0.46x-0.35x)=(P+12)-(P-10)$$ $$0.11x=22$$ x=220.11=200 

So, the total marks = 200

Now, Find the Pass Marks:

Use Equation 1:

0.35×200=P−10       

$$P=80$$

✅ Correct Answer: (3) 80

🔍 Summary Table

💡 Why This Is Useful

This type of problem:

• Tests your algebraic thinking

• Appears frequently in competitive exams (like SSC, Banking, GRE, etc.)

• Teaches you how to relate percentages and absolute marks

🎯 Key Takeaway

If you know the percentage scores and how much a student fails or passes by, you can easily calculate the total and pass marks using simple algebra.

Final Answer: Pass marks = 80