The total marks for a subject in an examination was 200. It had three components - theory, practical and project, the percentage weightages for the first and the third being 50 and 10 respectively. One of the criteria to pass the examination was to secure at least 60%, in practical. A student secured 42 in practical. How much percentage of the total marks should be given to him as grace so that he passes the exam?

Options

A. 3
B. 5
C. 4
D. 6

Answer

To solve the problem step by step, we will follow these calculations:

### Step 1: Determine the weightage of each component
The total marks for the subject is 200. The weightages for each component are:
- Theory: 50%
- Practical: (100% - 50% - 10%) = 40%
- Project: 10%

### Step 2: Calculate the marks allocated to each component
- Theory marks = 50% of 200 = 0.50 × 200 = 100 marks
- Practical marks = 40% of 200 = 0.40 × 200 = 80 marks
- Project marks = 10% of 200 = 0.10 × 200 = 20 marks

### Step 3: Determine the passing criteria for practical
To pass the examination, a student must secure at least 60% in practical.
- Minimum marks required in practical = 60% of 80 marks
= (60/100) × 80 = 48 marks

### Step 4: Identify the marks secured by the student
The student secured 42 marks in practical.

### Step 5: Calculate how many marks the student is short
Marks needed to pass = 48 marks
Marks secured = 42 marks
Marks short = 48 - 42 = 6 marks

### Step 6: Calculate the percentage of total marks needed as grace
To find out how much percentage of the total marks (200) should be given as grace:
- Grace marks needed = 6 marks
- Percentage of total marks = (Grace marks / Total marks) × 100
= (6 / 200) × 100 = 3%

### Final Answer
The student should be given 3% of the total marks as grace to pass the examination.

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