JAMIA 2023 — Mathematics PYQ

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Question

JAMIA 2023 — Mathematics PYQ

JAMIA | Mathematics | 2023

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

Choose the correct answer:

Explanation

Step 1: Find Enrollment in Mathematics ( $M$ )

We are given that 30 students represent 10% of the mathematics enrollment.

10\% \text{ of } M = 30

0.10 \times M = 30

M = \frac{30}{0.10} = 300

Step 2: Find Enrollment in Chemistry ( $C$ )

We are given that 30 students represent 12% of the chemistry enrollment.

12\% \text{ of } C = 30

0.12 \times C = 30

C = \frac{30}{0.12} = 250

Step 3: Identify the Intersection

The number of students taking both subjects is given as:

n(M \cap C) = 30

Step 4: Calculate Students taking At Least One Subject

To find the number of students taking at least one subject, we find the union $n(M \cup C)$ :

n(M \cup C) = n(M) + n(C) - n(M \cap C)

n(M \cup C) = 300 + 250 - 30

n(M \cup C) = 550 - 30

n(M \cup C) = 520

Final Answer:

The number of students who take at least one of these two subjects is 520.