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

Finding the Pass Mark Based on Test Scores

In this problem, we are given that a boy scored 35% marks and failed by 10 marks. If he had scored 46%, he would have passed by 12 marks. We are asked to determine the pass mark for the test.

Step-by-Step Solution:

1. Let the total marks of the test be $T$.

2. Score and Marks for 35%:

   • The boy’s score at 35% is $0.35T$.

   • According to the problem, he fails by 10 marks. This means the pass mark is $0.35T+10$.

3. Score and Marks for 46%:

   • The boy’s score at 46% is $0.46T$.

   • If he had scored 46%, he would have passed by 12 marks. This means:

     $$0.46T=0.35T+10+12=0.35T+22$$

4. Solve for $T$:

   • Now, we can solve the equation:

     $$0.46T-0.35T=22$$ $$0.11T=22$$ T=220.11=200T = \frac{22}{0.11} = 200T=0.1122​=200

5. Calculate the Pass Mark:

   • The pass mark is $0.35T+10$:

     $$0.35\times 200+10=70+10=80$$

✅ Correct Answer:

(3) 80

Conclusion:

The pass mark for the test is 80. By using the given percentages and the relationships between the scores, we were able to calculate the total marks of the test and the exact pass mark. This is a useful example of solving problems involving percentages and linear equations in everyday conte