Question

The number of students who take both the subjects mathematics and chemistry is 30. This represents 10% of the enrolment in mathematics and 12% of the enrolment in chemistry. How many students take at least one of these two subjects?

• A. 520
• B. 490
• C. 560
• D. 480

Hint:

To find the number of students taking at least one subject, use the formula: \[ |A \cup B| = |A| + |B| - |A \cap B| \] where \( A \) and \( B \) are the two subjects.

Answer 1

The Correct Option is A

Let the number of students who take only Mathematics be \( x \), and the number of students who take only Chemistry be \( y \). From the Venn diagram: - The total number of students in Mathematics is \( x + 30 \). - The total number of students in Chemistry is \( y + 30 \). Given conditions: \[ 30 = \frac{10}{100} (x + 30) \] Solving for \( x \): \[ x + 30 = \frac{30 \times 100}{10} = 300 \] \[ x = 270 \] Similarly, for Chemistry: \[ 30 = \frac{12}{100} (y + 30) \] Solving for \( y \): \[ y + 30 = \frac{30 \times 100}{12} = 250 \] \[ y = 220 \] Now, using the formula for the union of two sets: \[ |M \cup C| = |M| + |C| - |M \cap C| \] Substituting values: \[ x + y + 30 = 270 + 220 + 30 = 520 \] Thus, the final answer is: \[ \boxed{520} \]