Question

The number of students who take both the subjects mathematics and chemistry is 30. This represents 1% of the enrolment in mathematics and 12% of the enrolment in chemistry. How many students take at least one of these two subjects?
1. 520
2. 490
3. 560
4. 480
5. 540

Answer 1

Hint: According to the question it is asked to us to find out how many students take at least one of these subjects and the conditions are given to us for this. So, we will make the equations according to the given conditions and then we will solve these equations to get an exact answer.

Complete step-by-step solution:
It is given to us that the number of students who take both the subjects mathematics and chemistry is 30, and this represents 1% of the enrolment in mathematics and 12% of the enrolment in chemistry. So, if we make the equations according to the given data, then,
Let the number of students who take mathematics = $x$
And number of students who take chemistry = $y$
According to the question:
$\begin{align}
  & 0.10x=30\ldots \ldots \ldots \left( i \right) \\
 & 0.12y=30\ldots \ldots \ldots \left( ii \right) \\
\end{align}$
Now solving for $x$ and $y$, we get,
$\begin{align}
  & 0.10x=30 \\
 &\Rightarrow 10x=3000 \\
 &\Rightarrow x=300 \\
\end{align}$
And now solving for $y$, we get,
$\begin{align}
  & 0.12y=30 \\
 &\Rightarrow 12y=3000 \\
 &\Rightarrow y=250 \\
\end{align}$
So, the total number of students taking at least one of these two subjects will be,
$\begin{align}
  & x+y-30 \\
 & =300+250-30 \\
 & =550-30 \\
 & =520 \\
\end{align}$
Hence the total number of students for at least one subject is 520. Hence the correct answer is option 1.


Note: For solving these types of questions you have to be careful when you are making equations from the given data. If the equation is right then we can solve it properly and the answer will be right and if the equation will be wrong then the whole solution will be completely wrong.