Comprehension:
Read the data given and answer the following questions:
In a class of 60 students:
42 like Mathes,
32 like English,
12 like neither Maths nor English.
Students who like only Maths from what percentage of the total number of students in the class?

Options

A. 0.2667
B. 0.2422
C. 0.288
D. 0.3282

Answer

To solve the problem, we will follow these steps:

### Step 1: Understand the total number of students
We know that the total number of students in the class is 60.

### Step 2: Identify students who like neither subject
According to the problem, 12 students like neither Maths nor English.

### Step 3: Calculate students who like at least one subject
To find the number of students who like at least one subject (Maths or English), we subtract the number of students who like neither from the total number of students:
\[ \text{Students who like at least one subject} = \text{Total students} - \text{Students who like neither} \]
\[ = 60 - 12 = 48 \]

### Step 4: Use the formula for union of two sets
We can use the formula for the union of two sets:
\[ N(A \cup B) = N(A) + N(B) - N(A \cap B) \]
Where:
- \(N(A)\) = Number of students who like Maths = 42
- \(N(B)\) = Number of students who like English = 32
- \(N(A \cup B)\) = Students who like at least one subject = 48

### Step 5: Substitute the values into the formula
Substituting the known values into the formula:
\[ 48 = 42 + 32 - N(A \cap B) \]
\[ 48 = 74 - N(A \cap B) \]
\[ N(A \cap B) = 74 - 48 = 26 \]

### Step 6: Calculate students who like only Maths and only English
- Students who like only Maths:
\[ N(\text{Only Maths}) = N(A) - N(A \cap B) = 42 - 26 = 16 \]
- Students who like only English:
\[ N(\text{Only English}) = N(B) - N(A \cap B) = 32 - 26 = 6 \]

### Step 7: Calculate the percentage of students who like only Maths
To find the percentage of students who like only Maths in relation to the total number of students:
\[ \text{Percentage} = \left(\frac{N(\text{Only Maths})}{\text{Total students}}\right) \times 100 \]
\[ = \left(\frac{16}{60}\right) \times 100 \]
\[ = \frac{1600}{60} = \frac{80}{3} \approx 26.67\% \]

### Final Answer
The percentage of students who like only Maths is approximately **26.67%**.

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