Question

The number of students who take both the subjects Mathematics and Chemistry is $30$. This represents $10\%$ of the enrollment in Mathematics and $12\%$ of the enrollment in Chemistry. How many students take at least one of these two subjects?

• A. $520$
• B. $490$
• C. $560$
• D. $480$
• E. $540$

Answer 1

The correct option is A

$520$

Explanation for the correct option:

Find the required number of students

Let the number of students who has taken Mathematics $=x$

and the number of students who has taken Chemistry $=y$

According to question,

$$\begin{gathered} \left(\frac{10}{100}\right)x=\left(\frac{12}{100}\right)y=30 \\ \Rightarrow 0.10x=0.12y=30 \end{gathered}$$

Solving for$x$ and $y$ we get,

$0.10x=30$

$$\begin{gathered} \Rightarrow x=\frac{30}{0.10} \\ \Rightarrow x=300 \end{gathered}$$

and$0.12y=30$

$$\begin{gathered} \Rightarrow y=\frac{30}{0.12} \\ \Rightarrow y=250 \end{gathered}$$

$\therefore$Total number of students taken at least one of these two subjects $=300+250-30$

$=520$

Hence, option (A), $520$ is the correct answer.