Question:medium

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?

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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.
Updated On: Nov 26, 2025
  • 520
  • 490
  • 560
  • 480
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The Correct Option is A

Solution and Explanation

Let \( x \) represent the number of students taking only Mathematics, and \( y \) represent the number of students taking only Chemistry. 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 \( y \): \[ y + 30 = \frac{30 \times 100}{12} = 250 \] \[ y = 220 \] Using the formula for the union of two sets: \[ |M \cup C| = |M| + |C| - |M \cap C| \] Substituting values: The total number of students is \( x + y + 30 \), which equals \( 270 + 220 + 30 = 520 \). Thus, the final answer is: \[ \boxed{520} \]
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