Out of 80 students who secured first class marks in Matchematics or in Physics , 50 obtained first class marks in Mathematics and 10 in both Physics and Mathematics.
How many students secured first class marks in Physics only ?

Answer

To solve the problem of how many students secured first-class marks in Physics only, we can use the principle of sets and a Venn diagram. Let's break down the solution step by step.

### Step-by-Step Solution

1. **Identify the Total Number of Students:**
We know that there are a total of 80 students who secured first-class marks in either Mathematics or Physics.

**Hint:** Always start by identifying the total number of elements in the universal set.

2. **Identify Students Who Scored in Mathematics:**
It is given that 50 students obtained first-class marks in Mathematics.

**Hint:** Note the number of students in each individual set.

3. **Identify Students Who Scored in Both Subjects:**
It is also given that 10 students obtained first-class marks in both Mathematics and Physics.

**Hint:** This is important for understanding the overlap between the two sets.

4. **Calculate Students Who Scored Only in Mathematics:**
To find the number of students who scored only in Mathematics, we subtract the number of students who scored in both subjects from the total who scored in Mathematics:
\[ \text{Students in Mathematics only} = \text{Total in Mathematics} - \text{Students in both} \]
\[ \text{Students in Mathematics only} = 50 - 10 = 40 \]

**Hint:** This step helps to clarify how many students are exclusively in one set.

5. **Calculate Students Who Scored in Physics:**
Since the total number of students is 80, we can find the total number of students who scored in Physics by subtracting the number of students who scored only in Mathematics and those who scored in both subjects from the total:
\[ \text{Total in Physics} = \text{Total Students} - (\text{Students in Mathematics only} + \text{Students in both}) \]
\[ \text{Total in Physics} = 80 - (40 + 10) = 30 \]

**Hint:** This gives you the total number of students who scored in Physics, including those who scored in both subjects.

6. **Calculate Students Who Scored Only in Physics:**
To find the number of students who scored only in Physics, we subtract the number of students who scored in both subjects from the total number of students who scored in Physics:
\[ \text{Students in Physics only} = \text{Total in Physics} - \text{Students in both} \]
\[ \text{Students in Physics only} = 30 - 10 = 20 \]

**Hint:** This final calculation gives you the number of students who are exclusively in the Physics set.

### Final Answer:
The number of students who secured first-class marks in Physics only is **20**.