Question

Say true or false:
10 Students of Class X took part in a mathematics quiz. If the number of girls is 4 more than the number of boys, then the number of boys and girls who took part in the quiz are 3 and 7, respectively.
True
False

Answer 1

Hint: In this question, we will write one value in terms of another and form an equation, solving which we will get the required answer.

Complete step-by-step solution -
Ten students of Class X took part in a mathematics quiz, out of which some are boys and some are girls.
Let us consider that number of boys who took part in the mathematics quiz to be x.
Now, according to the given question, the number of girls who took part in mathematics out of ten students are 4 more than the number of boys who took part in mathematics quiz.
Then the number of girls will be \[4+x\] who participated in the quiz.
Since, total students who participated in quiz from Class X are 10; therefore, number of girls plus number of boys who participated will be 10. That is $x+\left( 4+x \right)=10$ .
Opening brackets, we get,
$\begin{align}
  & x+4+x=10 \\
 & \Rightarrow 2x+4=0 \\
\end{align}$
Subtracting 4 from both sides of the equation, we get,
$\begin{align}
  & 2x+4-4=10-4 \\
 & \Rightarrow 2x=6 \\
\end{align}$
Dividing 2 from both sides of equation, we get,
$\begin{align}
  & \dfrac{2x}{2}=\dfrac{6}{2} \\
 & \Rightarrow x=3 \\
\end{align}$
Hence, the number of boys who participated in the quiz are 3.
Number of girls who participated in the quiz are $4+3=7$.
Therefore, the given statement is true, that is the correct answer is option (a).

Note: In this type of question, you can also directly check given conditions in the given answers without actually solving them. Like in the given question, 7 is more than 3 and sum is 10, So, the statement is true.